Daily Papers

Object-centric reconstruction seeks to recover the 3D structure of a scene through composition of independent objects. While this independence can simplify modeling, it discards strong signals that could improve reconstruction, notably repetition where the same object model is seen multiple times in a scene, or across scans. We propose the Joint Reconstruction Model (JRM) to leverage repetition by framing object reconstruction as one of personalized generation: multiple observations share a common subject that should be consistent for all observations, while still adhering to the specific pose and state from each. Prior methods in this direction rely on explicit matching and rigid alignment across observations, making them sensitive to errors and difficult to extend to non-rigid transformations. In contrast, JRM is a 3D flow-matching generative model that implicitly aggregates unaligned observations in its latent space, learning to produce consistent and faithful reconstructions in a data-driven manner without explicit constraints. Evaluations on synthetic and real-world data show that JRM's implicit aggregation removes the need for explicit alignment, improves robustness to incorrect associations, and naturally handles non-rigid changes such as articulation. Overall, JRM outperforms both independent and alignment-based baselines in reconstruction quality.

In this paper, we introduce LATO, a novel topology-preserving latent representation that enables scalable, flow matching-based synthesis of explicit 3D meshes. LATO represents a mesh as a Vertex Displacement Field (VDF) anchored on surface, incorporating a sparse voxel Variational Autoencoder (VAE) to compress this explicit signal into a structured, topology-aware voxel latent. To decapsulate the mesh, the VAE decoder progressively subdivides and prunes latent voxels to instantiate precise vertex locations. In the end, a dedicated connection head queries the voxel latent to predict edge connectivity between vertex pairs directly, allowing mesh topology to be recovered without isosurface extraction or heuristic meshing. For generative modeling, LATO adopts a two-stage flow matching process, first synthesizing the structure voxels and subsequently refining the voxel-wise topology features. Compared to prior isosurface/triangle-based diffusion models and autoregressive generation approaches, LATO generates meshes with complex geometry, well-formed topology while being highly efficient in inference.

Segmenting 3D blood vessels is a critical yet challenging task in medical image analysis. This is due to significant imaging modality-specific variations in artifacts, vascular patterns and scales, signal-to-noise ratios, and background tissues. These variations, along with domain gaps arising from varying imaging protocols, limit the generalization of existing supervised learning-based methods, requiring tedious voxel-level annotations for each dataset separately. While foundation models promise to alleviate this limitation, they typically fail to generalize to the task of blood vessel segmentation, posing a unique, complex problem. In this work, we present vesselFM, a foundation model designed specifically for the broad task of 3D blood vessel segmentation. Unlike previous models, vesselFM can effortlessly generalize to unseen domains. To achieve zero-shot generalization, we train vesselFM on three heterogeneous data sources: a large, curated annotated dataset, data generated by a domain randomization scheme, and data sampled from a flow matching-based generative model. Extensive evaluations show that vesselFM outperforms state-of-the-art medical image segmentation foundation models across four (pre-)clinically relevant imaging modalities in zero-, one-, and few-shot scenarios, therefore providing a universal solution for 3D blood vessel segmentation.

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Earthquake hazard analysis and design of spatially distributed infrastructure, such as power grids and energy pipeline networks, require scenario-specific ground-motion time histories with realistic frequency content and spatiotemporal coherence. However, producing the large ensembles needed for uncertainty quantification with physics-based simulations is computationally intensive and impractical for engineering workflows. To address this challenge, we introduce Ground-Motion Flow (GMFlow), a physics-inspired latent operator flow matching framework that generates realistic, large-scale regional ground-motion time-histories conditioned on physical parameters. Validated on simulated earthquake scenarios in the San Francisco Bay Area, GMFlow generates spatially coherent ground motion across more than 9 million grid points in seconds, achieving a 10,000-fold speedup over the simulation workflow, which opens a path toward rapid and uncertainty-aware hazard assessment for distributed infrastructure. More broadly, GMFlow advances mesh-agnostic functional generative modeling and could potentially be extended to the synthesis of large-scale spatiotemporal physical fields in diverse scientific domains.

Flow matching models have emerged as a powerful method for generative modeling on domains like images or videos, and even on irregular or unstructured data like 3D point clouds or even protein structures. These models are commonly trained in two stages: first, a data compressor is trained, and in a subsequent training stage a flow matching generative model is trained in the latent space of the data compressor. This two-stage paradigm sets obstacles for unifying models across data domains, as hand-crafted compressors architectures are used for different data modalities. To this end, we introduce INRFlow, a domain-agnostic approach to learn flow matching transformers directly in ambient space. Drawing inspiration from INRs, we introduce a conditionally independent point-wise training objective that enables INRFlow to make predictions continuously in coordinate space. Our empirical results demonstrate that INRFlow effectively handles different data modalities such as images, 3D point clouds and protein structure data, achieving strong performance in different domains and outperforming comparable approaches. INRFlow is a promising step towards domain-agnostic flow matching generative models that can be trivially adopted in different data domains.

Designing metal-organic frameworks (MOFs) with novel chemistries is a longstanding challenge due to their large combinatorial space and complex 3D arrangements of the building blocks. While recent deep generative models have enabled scalable MOF generation, they assume (1) a fixed set of building blocks and (2) known local 3D coordinates of building blocks. However, this limits their ability to (1) design novel MOFs and (2) generate the structure using novel building blocks. We propose a two-stage MOF generation framework that overcomes these limitations by modeling both chemical and geometric degrees of freedom. First, we train an SMILES-based autoregressive model to generate metal and organic building blocks, paired with a cheminformatics toolkit for 3D structure initialization. Second, we introduce a flow matching model that predicts translations, rotations, and torsional angles to assemble the blocks into valid 3D frameworks. Our experiments demonstrate improved reconstruction accuracy, the generation of valid, novel, and unique MOFs, and the ability to create novel building blocks. Our code is available at https://github.com/nayoung10/MOFFlow-2.

Most recent advances in 3D generative modeling rely on diffusion or flow-matching formulations. We instead explore a fully autoregressive alternative and introduce GaussianGPT, a transformer-based model that directly generates 3D Gaussians via next-token prediction, thus facilitating full 3D scene generation. We first compress Gaussian primitives into a discrete latent grid using a sparse 3D convolutional autoencoder with vector quantization. The resulting tokens are serialized and modeled using a causal transformer with 3D rotary positional embedding, enabling sequential generation of spatial structure and appearance. Unlike diffusion-based methods that refine scenes holistically, our formulation constructs scenes step-by-step, naturally supporting completion, outpainting, controllable sampling via temperature, and flexible generation horizons. This formulation leverages the compositional inductive biases and scalability of autoregressive modeling while operating on explicit representations compatible with modern neural rendering pipelines, positioning autoregressive transformers as a complementary paradigm for controllable and context-aware 3D generation.

Brain Magnetic Resonance Imaging (MRI) plays a central role in studying neurological development, aging, and diseases. One key application is Brain Age Prediction (BAP), which estimates an individual's biological brain age from MRI data. Effective BAP models require large, diverse, and age-balanced datasets, whereas existing 3D MRI datasets are demographically skewed, limiting fairness and generalizability. Acquiring new data is costly and ethically constrained, motivating generative data augmentation. Current generative methods are often based on latent diffusion models, which operate in learned low dimensional latent spaces to address the memory demands of volumetric MRI data. However, these methods are typically slow at inference, may introduce artifacts due to latent compression, and are rarely conditioned on age, thereby affecting the BAP performance. In this work, we propose FlowLet, a conditional generative framework that synthesizes age-conditioned 3D MRIs by leveraging flow matching within an invertible 3D wavelet domain, helping to avoid reconstruction artifacts and reducing computational demands. Experiments show that FlowLet generates high-fidelity volumes with few sampling steps. Training BAP models with data generated by FlowLet improves performance for underrepresented age groups, and region-based analysis confirms preservation of anatomical structures.

General-purpose 3D chemical modeling encompasses molecules and materials, requiring both generative and predictive capabilities. However, most existing AI approaches are optimized for a single domain (molecules or materials) and a single task (generation or prediction), which limits representation sharing and transfer. We introduce Zatom-1, the first end-to-end, fully open-source foundation model that unifies generative and predictive learning of 3D molecules and materials. Zatom-1 is a Transformer trained with a multimodal flow matching objective that jointly models discrete atom types and continuous 3D geometries. This approach supports scalable pretraining with predictable gains as model capacity increases, while enabling fast and stable sampling. We use joint generative pretraining as a universal initialization for downstream multi-task prediction of properties, energies, and forces. Empirically, Zatom-1 matches or outperforms specialized baselines on both generative and predictive benchmarks, while reducing the generative inference time by more than an order of magnitude. Our experiments demonstrate positive predictive transfer between chemical domains from joint generative pretraining: modeling materials during pretraining improves molecular property prediction accuracy.

We present WUKONG, a novel training-free framework for high-fidelity textured 3D morphing that takes a pair of source and target prompts (image or text) as input. Unlike conventional methods -- which rely on manual correspondence matching and deformation trajectory estimation (limiting generalization and requiring costly preprocessing) -- WUKONG leverages the generative prior of flow-based transformers to produce high-fidelity 3D transitions with rich texture details. To ensure smooth shape transitions, we exploit the inherent continuity of flow-based generative processes and formulate morphing as an optimal transport barycenter problem. We further introduce a sequential initialization strategy to prevent abrupt geometric distortions and preserve identity coherence. For faithful texture preservation, we propose a similarity-guided semantic consistency mechanism that selectively retains high-frequency details and enables precise control over blending dynamics. This avoids common artifacts like oversmoothing while maintaining semantic fidelity. Extensive quantitative and qualitative evaluations demonstrate that WUKONG significantly outperforms state-of-the-art methods, achieving superior results across diverse geometry and texture variations.

Modern 3D generation methods can rapidly create shapes from sparse or single views, but their outputs often lack geometric detail due to computational constraints. We present DetailGen3D, a generative approach specifically designed to enhance these generated 3D shapes. Our key insight is to model the coarse-to-fine transformation directly through data-dependent flows in latent space, avoiding the computational overhead of large-scale 3D generative models. We introduce a token matching strategy that ensures accurate spatial correspondence during refinement, enabling local detail synthesis while preserving global structure. By carefully designing our training data to match the characteristics of synthesized coarse shapes, our method can effectively enhance shapes produced by various 3D generation and reconstruction approaches, from single-view to sparse multi-view inputs. Extensive experiments demonstrate that DetailGen3D achieves high-fidelity geometric detail synthesis while maintaining efficiency in training.

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods still face the challenges of expensive computing and a large number of function evaluations of off-the-shelf solvers in the pixel space. Furthermore, although latent-based generative methods have shown great success in recent years, this particular model type remains underexplored in this area. In this work, we propose to apply flow matching in the latent spaces of pretrained autoencoders, which offers improved computational efficiency and scalability for high-resolution image synthesis. This enables flow-matching training on constrained computational resources while maintaining their quality and flexibility. Additionally, our work stands as a pioneering contribution in the integration of various conditions into flow matching for conditional generation tasks, including label-conditioned image generation, image inpainting, and semantic-to-image generation. Through extensive experiments, our approach demonstrates its effectiveness in both quantitative and qualitative results on various datasets, such as CelebA-HQ, FFHQ, LSUN Church & Bedroom, and ImageNet. We also provide a theoretical control of the Wasserstein-2 distance between the reconstructed latent flow distribution and true data distribution, showing it is upper-bounded by the latent flow matching objective. Our code will be available at https://github.com/VinAIResearch/LFM.git.

We present HY-Motion 1.0, a series of state-of-the-art, large-scale, motion generation models capable of generating 3D human motions from textual descriptions. HY-Motion 1.0 represents the first successful attempt to scale up Diffusion Transformer (DiT)-based flow matching models to the billion-parameter scale within the motion generation domain, delivering instruction-following capabilities that significantly outperform current open-source benchmarks. Uniquely, we introduce a comprehensive, full-stage training paradigm -- including large-scale pretraining on over 3,000 hours of motion data, high-quality fine-tuning on 400 hours of curated data, and reinforcement learning from both human feedback and reward models -- to ensure precise alignment with the text instruction and high motion quality. This framework is supported by our meticulous data processing pipeline, which performs rigorous motion cleaning and captioning. Consequently, our model achieves the most extensive coverage, spanning over 200 motion categories across 6 major classes. We release HY-Motion 1.0 to the open-source community to foster future research and accelerate the transition of 3D human motion generation models towards commercial maturity.

LiDAR scene synthesis is an emerging solution to scarcity in 3D data for robotic tasks such as autonomous driving. Recent approaches employ diffusion or flow matching models to generate realistic scenes, but 3D data remains limited compared to RGB datasets with millions of samples. We introduce R3DPA, the first LiDAR scene generation method to unlock image-pretrained priors for LiDAR point clouds, and leverage self-supervised 3D representations for state-of-the-art results. Specifically, we (i) align intermediate features of our generative model with self-supervised 3D features, which substantially improves generation quality; (ii) transfer knowledge from large-scale image-pretrained generative models to LiDAR generation, mitigating limited LiDAR datasets; and (iii) enable point cloud control at inference for object inpainting and scene mixing with solely an unconditional model. On the KITTI-360 benchmark R3DPA achieves state of the art performance. Code and pretrained models are available at https://github.com/valeoai/R3DPA.

Unbounded 3D world generation is emerging as a foundational task for scene modeling in computer vision, graphics, and robotics. In this work, we present WorldFlow3D, a novel method capable of generating unbounded 3D worlds. Building upon a foundational property of flow matching - namely, defining a path of transport between two data distributions - we model 3D generation more generally as a problem of flowing through 3D data distributions, not limited to conditional denoising. We find that our latent-free flow approach generates causal and accurate 3D structure, and can use this as an intermediate distribution to guide the generation of more complex structure and high-quality texture - all while converging more rapidly than existing methods. We enable controllability over generated scenes with vectorized scene layout conditions for geometric structure control and visual texture control through scene attributes. We confirm the effectiveness of WorldFlow3D on both real outdoor driving scenes and synthetic indoor scenes, validating cross-domain generalizability and high-quality generation on real data distributions. We confirm favorable scene generation fidelity over approaches in all tested settings for unbounded scene generation. For more, see https://light.princeton.edu/worldflow3d.

Recent advancements in 3D generative modeling have significantly improved the generation realism, yet the field is still hampered by existing representations, which struggle to capture assets with complex topologies and detailed appearance. This paper present an approach for learning a structured latent representation from native 3D data to address this challenge. At its core is a new sparse voxel structure called O-Voxel, an omni-voxel representation that encodes both geometry and appearance. O-Voxel can robustly model arbitrary topology, including open, non-manifold, and fully-enclosed surfaces, while capturing comprehensive surface attributes beyond texture color, such as physically-based rendering parameters. Based on O-Voxel, we design a Sparse Compression VAE which provides a high spatial compression rate and a compact latent space. We train large-scale flow-matching models comprising 4B parameters for 3D generation using diverse public 3D asset datasets. Despite their scale, inference remains highly efficient. Meanwhile, the geometry and material quality of our generated assets far exceed those of existing models. We believe our approach offers a significant advancement in 3D generative modeling.

Reconstructing the complete geometry of a scene from a single RGB image remains challenging - especially when inferring hidden structures where visual evidence is incomplete. We introduce VolFill, a generative framework that predicts the 3D structure of the complete scene rather than relying on traditional pixel-aligned regression. Our method utilizes a hybrid 3D VAE to compress sparse truncated unsigned distance function grids into a compact latent space, paired with a latent Diffusion Transformer that denoises this representation to recover the complete scene. We condition the generation on geometry foundation models, leveraging rich spatial priors for robust reasoning. Unlike existing methods limited by per-ray constraints or unstructured point-cloud queries, VolFill provides a structured representation that supports direct surface extraction and occupancy queries at scale. Extensive experiments on the SCRREAM and NRGB-D datasets demonstrate that our approach significantly outperforms current baselines, providing a robust foundation for holistic spatial understanding.

Synthesizability remains a critical bottleneck in generative molecular design. While recent advances have addressed synthesizability in 2D graphs, extending these constraints to 3D for geometry-based conditional generation remains largely unexplored. In this work, we present SynCoGen (Synthesizable Co-Generation), a single framework that combines simultaneous masked graph diffusion and flow matching for synthesizable 3D molecule generation. SynCoGen samples from the joint distribution of molecular building blocks, chemical reactions, and atomic coordinates. To train the model, we curated SynSpace, a dataset family containing over 1.2M synthesis-aware building block graphs and 7.5M conformers. SynCoGen achieves state-of-the-art performance in unconditional small molecule graph and conformer co-generation. For protein ligand generation in drug discovery, the amortized model delivers superior performance in both molecular linker design and pharmacophore-conditioned generation across diverse targets without relying on any scoring functions. Overall, this multimodal non-autoregressive formulation represents a foundation for a range of molecular design applications, including analog expansion, lead optimization, and direct de novo design.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

Despite the remarkable developments achieved by recent 3D generation works, scaling these methods to geographic extents, such as modeling thousands of square kilometers of Earth's surface, remains an open challenge. We address this through a dual innovation in data infrastructure and model architecture. First, we introduce Aerial-Earth3D, the largest 3D aerial dataset to date, consisting of 50k curated scenes (each measuring 600m x 600m) captured across the U.S. mainland, comprising 45M multi-view Google Earth frames. Each scene provides pose-annotated multi-view images, depth maps, normals, semantic segmentation, and camera poses, with explicit quality control to ensure terrain diversity. Building on this foundation, we propose EarthCrafter, a tailored framework for large-scale 3D Earth generation via sparse-decoupled latent diffusion. Our architecture separates structural and textural generation: 1) Dual sparse 3D-VAEs compress high-resolution geometric voxels and textural 2D Gaussian Splats (2DGS) into compact latent spaces, largely alleviating the costly computation suffering from vast geographic scales while preserving critical information. 2) We propose condition-aware flow matching models trained on mixed inputs (semantics, images, or neither) to flexibly model latent geometry and texture features independently. Extensive experiments demonstrate that EarthCrafter performs substantially better in extremely large-scale generation. The framework further supports versatile applications, from semantic-guided urban layout generation to unconditional terrain synthesis, while maintaining geographic plausibility through our rich data priors from Aerial-Earth3D. Our project page is available at https://whiteinblue.github.io/earthcrafter/

Deep generative models have shown promise for modeling metal-organic frameworks (MOFs), but existing approaches (1) rely on coarse-grained representations that assume fixed bond lengths and angles, and (2) neglect the MOF-adsorbate interactions, which are critical for downstream applications. We introduce AtomMOF, a scalable flow-based model built on an all-atom Diffusion Transformer that maps 2D molecular graphs of building blocks and adsorbates directly to equilibrium 3D structures without imposing structural constraints. We further present scaling laws for porous crystal generation, indicating predictable performance gains with increased model capacity, and introduce Feynman-Kac steering guided by machine-learned interatomic potentials to improve geometric validity and sampling stability. On the (MOF-only) BW dataset, AtomMOF increases the match rate by 35.00% and reduces RMSD by 32.64%. On the ODAC25 dataset (MOF-adsorbate), AtomMOF is substantially more sample-efficient than grand canonical Monte Carlo in recovering adsorption configurations and can identify candidates with lower adsorption energies than the reference dataset. Code is available at https://github.com/nayoung10/AtomMOF.

Existing generative models for 3D shapes can synthesize high-fidelity and visually plausible shapes. For certain classes of shapes that have undergone an engineering design process, the realism of the shape is tightly coupled with the underlying physical properties, e.g., aerodynamic efficiency for automobiles. Since existing methods lack knowledge of such physics, they are unable to use this knowledge to enhance the realism of shape generation. Motivated by this, we propose a unified physics-based 3D shape generation pipeline, with a focus on industrial design applications. Specifically, we introduce a new flow matching model with explicit physical guidance, consisting of an alternating update process. We iteratively perform a velocity-based update and a physics-based refinement, progressively adjusting the latent code to align with the desired 3D shapes and physical properties. We further strengthen physical validity by incorporating a physics-aware regularization term into the velocity-based update step. To support such physics-guided updates, we build a shape-and-physics variational autoencoder (SP-VAE) that jointly encodes shape and physics information into a unified latent space. The experiments on three benchmarks show that this synergistic formulation improves shape realism beyond mere visual plausibility.

High-fidelity 3D asset generation is crucial for various industries. While recent 3D pretrained models show strong capability in producing realistic content, most are built upon diffusion models and follow a two-stage pipeline that first generates geometry and then synthesizes appearance. Such a decoupled design tends to produce geometry-texture misalignment and non-negligible cost. In this paper, we propose UniLat3D, a unified framework that encodes geometry and appearance in a single latent space, enabling direct single-stage generation. Our key contribution is a geometry-appearance Unified VAE, which compresses high-resolution sparse features into a compact latent representation -- UniLat. UniLat integrates structural and visual information into a dense low-resolution latent, which can be efficiently decoded into diverse 3D formats, e.g., 3D Gaussians and meshes. Based on this unified representation, we train a single flow-matching model to map Gaussian noise directly into UniLat, eliminating redundant stages. Trained solely on public datasets, UniLat3D produces high-quality 3D assets in seconds from a single image, achieving superior appearance fidelity and geometric quality. More demos \& code are available at https://unilat3d.github.io/

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

Despite recent advances in 3D human motion generation (MoGen) on standard benchmarks, existing models still face a fundamental bottleneck in their generalization capability. In contrast, adjacent generative fields, most notably video generation (ViGen), have demonstrated remarkable generalization in modeling human behaviors, highlighting transferable insights that MoGen can leverage. Motivated by this observation, we present a comprehensive framework that systematically transfers knowledge from ViGen to MoGen across three key pillars: data, modeling, and evaluation. First, we introduce ViMoGen-228K, a large-scale dataset comprising 228,000 high-quality motion samples that integrates high-fidelity optical MoCap data with semantically annotated motions from web videos and synthesized samples generated by state-of-the-art ViGen models. The dataset includes both text-motion pairs and text-video-motion triplets, substantially expanding semantic diversity. Second, we propose ViMoGen, a flow-matching-based diffusion transformer that unifies priors from MoCap data and ViGen models through gated multimodal conditioning. To enhance efficiency, we further develop ViMoGen-light, a distilled variant that eliminates video generation dependencies while preserving strong generalization. Finally, we present MBench, a hierarchical benchmark designed for fine-grained evaluation across motion quality, prompt fidelity, and generalization ability. Extensive experiments show that our framework significantly outperforms existing approaches in both automatic and human evaluations. The code, data, and benchmark will be made publicly available.

Existing 3D generative models predominantly rely on implicit volumetric representations, which enforce watertight topology and struggle to represent thin-shell and non-manifold geometries such as garments. Geometry image-based approaches offer a surface-centric alternative, but existing methods rely on discrete binary occupancy maps whose resolution-dependent boundary encoding causes staircase artifacts and information loss upon downsampling, while surface reconstruction remains a non-differentiable post-processing step disconnected from the learning pipeline. To address this, we propose Differentiable Geometry Image (DiffGI), an end-to-end 3D-to-2D mapping framework that seamlessly integrates surface representation and geometric optimization. DiffGI replaces binary maps with a continuous 2D Truncated Signed Distance Function (TSDF), which encodes boundary position at subpixel precision within a fixed grid resolution, eliminating resolution-dependent staircase artifacts even under aggressive downsampling. Building on this continuous field, we introduce a differentiable Marching Squares algorithm based on analytical linear interpolation, allowing gradients from 3D surface losses to propagate back to the 2D latent space. Leveraging this differentiable pipeline, we train a DiffGI-VAE augmented with a geometry-aware normal rendering loss to compress complex 3D surfaces into an ultra-compact 32X32 latent space, and instantiate a transformer-based latent diffusion model with a flow-matching objective on top of this space for conditional 3D generation. Extensive experiments on garment and object datasets demonstrate that our method achieves superior reconstruction fidelity and boundary precision compared to prior geometry-image and voxel-based approaches, while requiring significantly fewer computational resources.

This paper presents improved native unified multimodal models, i.e., Show-o2, that leverage autoregressive modeling and flow matching. Built upon a 3D causal variational autoencoder space, unified visual representations are constructed through a dual-path of spatial (-temporal) fusion, enabling scalability across image and video modalities while ensuring effective multimodal understanding and generation. Based on a language model, autoregressive modeling and flow matching are natively applied to the language head and flow head, respectively, to facilitate text token prediction and image/video generation. A two-stage training recipe is designed to effectively learn and scale to larger models. The resulting Show-o2 models demonstrate versatility in handling a wide range of multimodal understanding and generation tasks across diverse modalities, including text, images, and videos. Code and models are released at https://github.com/showlab/Show-o.

3D Gaussian splatting enables high-quality novel view synthesis (NVS) at real-time frame rates. However, its quality drops sharply as we depart from the training views. Thus, dense captures are needed to match the high-quality expectations of some applications, e.g. Virtual Reality (VR). However, such dense captures are very laborious and expensive to obtain. Existing works have explored using 2D generative models to alleviate this requirement by distillation or generating additional training views. These methods are often conditioned only on a handful of reference input views and thus do not fully exploit the available 3D information, leading to inconsistent generation results and reconstruction artifacts. To tackle this problem, we propose a multi-view, flow matching model that learns a flow to connect novel view renderings from possibly sparse reconstructions to renderings that we expect from dense reconstructions. This enables augmenting scene captures with novel, generated views to improve reconstruction quality. Our model is trained on a novel dataset of 3.6M image pairs and can process up to 45 views at 540x960 resolution (91K tokens) on one H100 GPU in a single forward pass. Our pipeline consistently improves NVS in sparse- and dense-view scenarios, leading to higher-quality reconstructions than prior works across multiple, widely-used NVS benchmarks.

We propose a 3D latent representation that jointly models object geometry and view-dependent appearance. Most prior works focus on either reconstructing 3D geometry or predicting view-independent diffuse appearance, and thus struggle to capture realistic view-dependent effects. Our approach leverages that RGB-depth images provide samples of a surface light field. By encoding random subsamples of this surface light field into a compact set of latent vectors, our model learns to represent both geometry and appearance within a unified 3D latent space. This representation reproduces view-dependent effects such as specular highlights and Fresnel reflections under complex lighting. We further train a latent flow matching model on this representation to learn its distribution conditioned on a single input image, enabling the generation of 3D objects with appearances consistent with the lighting and materials in the input. Experiments show that our approach achieves higher visual quality and better input fidelity than existing methods.

We propose Perceptual Flow Matching (PFM), a simple yet effective framework for few-step generation in flow-matching models. Rather than performing velocity regression in the conventional VAE latent space, PFM supervises flow matching in a perceptual feature space using pretrained perceptual models. This simple change substantially improves the few-step generation capability of flow-matching models, reducing the number of sampling steps from 35-50 to 4-8 while preserving generation quality. Unlike existing acceleration and distillation approaches, PFM requires neither teacher models nor auxiliary score networks and can be integrated into standard flow-matching training pipelines with minimal modifications. Extensive experiments on image generation, video generation, and image editing tasks demonstrate that PFM consistently produces high-quality results while producing fewer artifacts than existing distillation-based methods. We further show that perceptual supervision shifts the regression minimizer from mean-seeking to mode-seeking, biasing predictions toward on-manifold modes that remain accurate under coarse few-step integration. Our results reveal that standard flow-matching training can naturally yield high-quality few-step generators when supervised in an appropriate representation space. We hope this insight inspires future research into representation-aware objectives for efficient generative modeling.

We introduce a novel generative model for video prediction based on latent flow matching, an efficient alternative to diffusion-based models. In contrast to prior work, we keep the high costs of modeling the past during training and inference at bay by conditioning only on a small random set of past frames at each integration step of the image generation process. Moreover, to enable the generation of high-resolution videos and to speed up the training, we work in the latent space of a pretrained VQGAN. Finally, we propose to approximate the initial condition of the flow ODE with the previous noisy frame. This allows to reduce the number of integration steps and hence, speed up the sampling at inference time. We call our model Random frame conditioned flow Integration for VidEo pRediction, or, in short, RIVER. We show that RIVER achieves superior or on par performance compared to prior work on common video prediction benchmarks, while requiring an order of magnitude fewer computational resources.

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.

Recent AI-based 3D content creation has largely evolved along two paths: feed-forward image-to-3D reconstruction approaches and 3D generative models trained with 2D or 3D supervision. In this work, we show that existing feed-forward reconstruction methods can serve as effective latent encoders for training 3D generative models, thereby bridging these two paradigms. By reusing powerful pre-trained reconstruction models, we avoid computationally expensive encoder network training and obtain rich 3D latent features for generative modeling for free. However, the latent spaces of reconstruction models are not well-suited for generative modeling due to their unstructured nature. To enable flow-based model training on these latent features, we develop post-processing pipelines, including protocols to standardize the features and spatial weighting to concentrate on important regions. We further incorporate a 2D image space perceptual rendering loss to handle the high-dimensional latent spaces. Finally, we propose a multi-stream transformer-based rectified flow architecture to achieve linear scaling and high-quality text-conditioned 3D generation. Our framework leverages the advancements of feed-forward reconstruction models to enhance the scalability of 3D generative modeling, achieving both high computational efficiency and state-of-the-art performance in text-to-3D generation.

Flow Matching (FM) algorithm achieves remarkable results in generative tasks especially in robotic manipulation. Building upon the foundations of diffusion models, the simulation-free paradigm of FM enables simple and efficient training, but inherently introduces a train-inference gap. Specifically, we cannot assess the model's output during the training phase. In contrast, other generative models including Variational Autoencoder (VAE), Normalizing Flow and Generative Adversarial Networks (GANs) directly optimize on the reconstruction loss. Such a gap is particularly evident in scenarios that demand high precision, such as robotic manipulation. Moreover, we show that FM's over-pursuit of straight predefined paths may introduce some serious problems such as stiffness into the system. These motivate us to fine-tune FM via Maximum Likelihood Estimation of reconstructions - an approach made feasible by FM's underlying smooth ODE formulation, in contrast to the stochastic differential equations (SDEs) used in diffusion models. This paper first theoretically analyzes the relation between training loss and inference error in FM. Then we propose a method of fine-tuning FM via Maximum Likelihood Estimation of reconstructions, which includes both straightforward fine-tuning and residual-based fine-tuning approaches. Furthermore, through specifically designed architectures, the residual-based fine-tuning can incorporate the contraction property into the model, which is crucial for the model's robustness and interpretability. Experimental results in image generation and robotic manipulation verify that our method reliably improves the inference performance of FM.

Simulation-free methods for training continuous-time generative models construct probability paths that go between noise distributions and individual data samples. Recent works, such as Flow Matching, derived paths that are optimal for each data sample. However, these algorithms rely on independent data and noise samples, and do not exploit underlying structure in the data distribution for constructing probability paths. We propose Multisample Flow Matching, a more general framework that uses non-trivial couplings between data and noise samples while satisfying the correct marginal constraints. At very small overhead costs, this generalization allows us to (i) reduce gradient variance during training, (ii) obtain straighter flows for the learned vector field, which allows us to generate high-quality samples using fewer function evaluations, and (iii) obtain transport maps with lower cost in high dimensions, which has applications beyond generative modeling. Importantly, we do so in a completely simulation-free manner with a simple minimization objective. We show that our proposed methods improve sample consistency on downsampled ImageNet data sets, and lead to better low-cost sample generation.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

Recently, Flow Matching models have pushed the boundaries of high-fidelity data generation across a wide range of domains. It typically employs a single large network to learn the entire generative trajectory from noise to data. Despite their effectiveness, this design struggles to capture distinct signal characteristics across timesteps simultaneously and incurs substantial inference costs due to the iterative evaluation of the entire model. To address these limitations, we propose Blockwise Flow Matching (BFM), a novel framework that partitions the generative trajectory into multiple temporal segments, each modeled by smaller but specialized velocity blocks. This blockwise design enables each block to specialize effectively in its designated interval, improving inference efficiency and sample quality. To further enhance generation fidelity, we introduce a Semantic Feature Guidance module that explicitly conditions velocity blocks on semantically rich features aligned with pretrained representations. Additionally, we propose a lightweight Feature Residual Approximation strategy that preserves semantic quality while significantly reducing inference cost. Extensive experiments on ImageNet 256x256 demonstrate that BFM establishes a substantially improved Pareto frontier over existing Flow Matching methods, achieving 2.1x to 4.9x accelerations in inference complexity at comparable generation performance. Code is available at https://github.com/mlvlab/BFM.

Flow Matching (FM) is a recent framework for generative modeling that has achieved state-of-the-art performance across various domains, including image, video, audio, speech, and biological structures. This guide offers a comprehensive and self-contained review of FM, covering its mathematical foundations, design choices, and extensions. By also providing a PyTorch package featuring relevant examples (e.g., image and text generation), this work aims to serve as a resource for both novice and experienced researchers interested in understanding, applying and further developing FM.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach has not yet led to comparable fidelity. There are several key obstacles: (i) the encoding into a lower-dimensional latent space makes the underlying (forward) mapping non-linear; (ii) the data likelihood term is usually intractable; and (iii) learned generative models struggle to recover rare, atypical data modes during inference. We present FLAIR, a novel training free variational framework that leverages flow-based generative models as a prior for inverse problems. To that end, we introduce a variational objective for flow matching that is agnostic to the type of degradation, and combine it with deterministic trajectory adjustments to recover atypical modes. To enforce exact consistency with the observed data, we decouple the optimization of the data fidelity and regularization terms. Moreover, we introduce a time-dependent calibration scheme in which the strength of the regularization is modulated according to off-line accuracy estimates. Results on standard imaging benchmarks demonstrate that FLAIR consistently outperforms existing diffusion- and flow-based methods in terms of reconstruction quality and sample diversity.

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although inverse problem solving has been extensively explored using diffusion models, it has not been rigorously examined within the broader context of flow models. Therefore, here we extend the diffusion inverse solvers (DIS) - which perform posterior sampling by combining a denoising diffusion prior with an likelihood gradient - into the flow framework. Specifically, by driving the flow-version of Tweedie's formula, we decompose the flow ODE into two components: one for clean image estimation and the other for noise estimation. By integrating the likelihood gradient and stochastic noise into each component, respectively, we demonstrate that posterior sampling for inverse problem solving can be effectively achieved using flows. Our proposed solver, Flow-Driven Posterior Sampling (FlowDPS), can also be seamlessly integrated into a latent flow model with a transformer architecture. Across four linear inverse problems, we confirm that FlowDPS outperforms state-of-the-art alternatives, all without requiring additional training.

Recent advances in generative modeling have demonstrated strong promise for high-quality point cloud upsampling. In this work, we present PUFM++, an enhanced flow-matching framework for reconstructing dense and accurate point clouds from sparse, noisy, and partial observations. PUFM++ improves flow matching along three key axes: (i) geometric fidelity, (ii) robustness to imperfect input, and (iii) consistency with downstream surface-based tasks. We introduce a two-stage flow-matching strategy that first learns a direct, straight-path flow from sparse inputs to dense targets, and then refines it using noise-perturbed samples to approximate the terminal marginal distribution better. To accelerate and stabilize inference, we propose a data-driven adaptive time scheduler that improves sampling efficiency based on interpolation behavior. We further impose on-manifold constraints during sampling to ensure that generated points remain aligned with the underlying surface. Finally, we incorporate a recurrent interface network~(RIN) to strengthen hierarchical feature interactions and boost reconstruction quality. Extensive experiments on synthetic benchmarks and real-world scans show that PUFM++ sets a new state of the art in point cloud upsampling, delivering superior visual fidelity and quantitative accuracy across a wide range of tasks. Code and pretrained models are publicly available at https://github.com/Holmes-Alan/Enhanced_PUFM.

Monocular depth estimation is crucial for numerous downstream vision tasks and applications. Current discriminative approaches to this problem are limited due to blurry artifacts, while state-of-the-art generative methods suffer from slow sampling due to their SDE nature. Rather than starting from noise, we seek a direct mapping from input image to depth map. We observe that this can be effectively framed using flow matching, since its straight trajectories through solution space offer efficiency and high quality. Our study demonstrates that a pre-trained image diffusion model can serve as an adequate prior for a flow matching depth model, allowing efficient training on only synthetic data to generalize to real images. We find that an auxiliary surface normals loss further improves the depth estimates. Due to the generative nature of our approach, our model reliably predicts the confidence of its depth estimates. On standard benchmarks of complex natural scenes, our lightweight approach exhibits state-of-the-art performance at favorable low computational cost despite only being trained on little synthetic data.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice generative quality. We bridge this gap by proposing Structured Coupling for Flow Matching (SCFM), a cooperative framework that augments flow matching with structured latent representation learning. By introducing structured latent variables and exogenous noise into the source, SCFM jointly learns a structured prior (via latent variable modeling) and a continuous transport map (via flow matching). It uses a shared time-dependent recognition network for both latent variable model variational inference and intermediate-time flow velocity estimation. This yields a structurally informed yet unconditional, simulation-free flow model, where the latent variable model can also assist flow sampling. Empirically, SCFM facilitates unsupervised latent representation learning for clustering, disentanglement and downstream tasks, while remaining competitive with flow matching in sample quality, showing that meaningful structure can be learned without sacrificing generative fidelity.

Flow matching casts sample generation as learning a continuous-time velocity field that transports noise to data. Existing flow matching networks typically predict each point's velocity independently, considering only its location and time along its flow trajectory, and ignoring neighboring points. However, this pointwise approach may overlook correlations between points along the generation trajectory that could enhance velocity predictions, thereby improving downstream generation quality. To address this, we propose Graph Flow Matching (GFM), a lightweight enhancement that decomposes the learned velocity into a reaction term -- any standard flow matching network -- and a diffusion term that aggregates neighbor information via a graph neural module. This reaction-diffusion formulation retains the scalability of deep flow models while enriching velocity predictions with local context, all at minimal additional computational cost. Operating in the latent space of a pretrained variational autoencoder, GFM consistently improves Fr\'echet Inception Distance (FID) and recall across five image generation benchmarks (LSUN Church, LSUN Bedroom, FFHQ, AFHQ-Cat, and CelebA-HQ at 256times256), demonstrating its effectiveness as a modular enhancement to existing flow matching architectures.

Flow matching is a powerful framework for generating high-quality samples in various applications, especially image synthesis. However, the intensive computational demands of these models, especially during the fine-tuning process and sampling processes, pose significant challenges for low-resource scenarios. This paper introduces Bellman Optimal Step-size Straightening (BOSS) technique for distilling flow-matching generative models: it aims specifically for a few-step efficient image sampling while adhering to a computational budget constraint. First, this technique involves a dynamic programming algorithm that optimizes the step sizes of the pretrained network. Then, it refines the velocity network to match the optimal step sizes, aiming to straighten the generation paths. Extensive experimental evaluations across image generation tasks demonstrate the efficacy of BOSS in terms of both resource utilization and image quality. Our results reveal that BOSS achieves substantial gains in efficiency while maintaining competitive sample quality, effectively bridging the gap between low-resource constraints and the demanding requirements of flow-matching generative models. Our paper also fortifies the responsible development of artificial intelligence, offering a more sustainable generative model that reduces computational costs and environmental footprints. Our code can be found at https://github.com/nguyenngocbaocmt02/BOSS.

Modern 3D generation methods can rapidly create shapes from sparse or single views, but their outputs often lack geometric detail due to computational constraints. We present DetailGen3D, a generative approach specifically designed to enhance these generated 3D shapes. Our key insight is to model the coarse-to-fine transformation directly through data-dependent flows in latent space, avoiding the computational overhead of large-scale 3D generative models. We introduce a token matching strategy that ensures accurate spatial correspondence during refinement, enabling local detail synthesis while preserving global structure. By carefully designing our training data to match the characteristics of synthesized coarse shapes, our method can effectively enhance shapes produced by various 3D generation and reconstruction approaches, from single-view to sparse multi-view inputs. Extensive experiments demonstrate that DetailGen3D achieves high-fidelity geometric detail synthesis while maintaining efficiency in training.

Flow matching has emerged as a promising framework for training generative models, demonstrating impressive empirical performance while offering relative ease of training compared to diffusion-based models. However, this method still requires numerous function evaluations in the sampling process. To address these limitations, we introduce a self-corrected flow distillation method that effectively integrates consistency models and adversarial training within the flow-matching framework. This work is a pioneer in achieving consistent generation quality in both few-step and one-step sampling. Our extensive experiments validate the effectiveness of our method, yielding superior results both quantitatively and qualitatively on CelebA-HQ and zero-shot benchmarks on the COCO dataset. Our implementation is released at https://github.com/VinAIResearch/SCFlow

Transferring appearance to 3D assets using different representations of the appearance object - such as images or text - has garnered interest due to its wide range of applications in industries like gaming, augmented reality, and digital content creation. However, state-of-the-art methods still fail when the geometry between the input and appearance objects is significantly different. A straightforward approach is to directly apply a 3D generative model, but we show that this ultimately fails to produce appealing results. Instead, we propose a principled approach inspired by universal guidance. Given a pretrained rectified flow model conditioned on image or text, our training-free method interacts with the sampling process by periodically adding guidance. This guidance can be modeled as a differentiable loss function, and we experiment with two different types of guidance including part-aware losses for appearance and self-similarity. Our experiments show that our approach successfully transfers texture and geometric details to the input 3D asset, outperforming baselines both qualitatively and quantitatively. We also show that traditional metrics are not suitable for evaluating the task due to their inability of focusing on local details and comparing dissimilar inputs, in absence of ground truth data. We thus evaluate appearance transfer quality with a GPT-based system objectively ranking outputs, ensuring robust and human-like assessment, as further confirmed by our user study. Beyond showcased scenarios, our method is general and could be extended to different types of diffusion models and guidance functions.

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, physics-informed generative tasks, and imaging inverse problems demonstrate the effectiveness and flexibility of the proposed framework.

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this work, we present Discrete Flow Matching, a novel discrete flow paradigm designed specifically for generating discrete data. Discrete Flow Matching offers several key contributions: (i) it works with a general family of probability paths interpolating between source and target distributions; (ii) it allows for a generic formula for sampling from these probability paths using learned posteriors such as the probability denoiser (x-prediction) and noise-prediction (epsilon-prediction); (iii) practically, focusing on specific probability paths defined with different schedulers considerably improves generative perplexity compared to previous discrete diffusion and flow models; and (iv) by scaling Discrete Flow Matching models up to 1.7B parameters, we reach 6.7% Pass@1 and 13.4% Pass@10 on HumanEval and 6.7% Pass@1 and 20.6% Pass@10 on 1-shot MBPP coding benchmarks. Our approach is capable of generating high-quality discrete data in a non-autoregressive fashion, significantly closing the gap between autoregressive models and discrete flow models.

Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood on standard benchmarks. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient realistic-looking synthesis and manipulation of large images. The code for our model is available at https://github.com/openai/glow

Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

We present Hunyuan3D 2.0, an advanced large-scale 3D synthesis system for generating high-resolution textured 3D assets. This system includes two foundation components: a large-scale shape generation model -- Hunyuan3D-DiT, and a large-scale texture synthesis model -- Hunyuan3D-Paint. The shape generative model, built on a scalable flow-based diffusion transformer, aims to create geometry that properly aligns with a given condition image, laying a solid foundation for downstream applications. The texture synthesis model, benefiting from strong geometric and diffusion priors, produces high-resolution and vibrant texture maps for either generated or hand-crafted meshes. Furthermore, we build Hunyuan3D-Studio -- a versatile, user-friendly production platform that simplifies the re-creation process of 3D assets. It allows both professional and amateur users to manipulate or even animate their meshes efficiently. We systematically evaluate our models, showing that Hunyuan3D 2.0 outperforms previous state-of-the-art models, including the open-source models and closed-source models in geometry details, condition alignment, texture quality, and etc. Hunyuan3D 2.0 is publicly released in order to fill the gaps in the open-source 3D community for large-scale foundation generative models. The code and pre-trained weights of our models are available at: https://github.com/Tencent/Hunyuan3D-2

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors. Our method first pretrains a flow model on the target features to capture the underlying distribution. This fixed flow model subsequently regularizes the latent space via an alignment loss, which reformulates the flow matching objective to treat the latents as optimization targets. We formally prove that minimizing this alignment loss establishes a computationally tractable surrogate objective for maximizing a variational lower bound on the log-likelihood of latents under the target distribution. Notably, the proposed method eliminates computationally expensive likelihood evaluations and avoids ODE solving during optimization. As a proof of concept, we demonstrate in a controlled setting that the alignment loss landscape closely approximates the negative log-likelihood of the target distribution. We further validate the effectiveness of our approach through large-scale image generation experiments on ImageNet with diverse target distributions, accompanied by detailed discussions and ablation studies. With both theoretical and empirical validation, our framework paves a new way for latent space alignment.

Modern continuous-time generative models typically induce V-shaped flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the hierarchical structures that exist in real-world data. To address this, we introduce Y-shaped generative flows, a framework in which samples travel together along shared pathways before branching off to target-specific endpoints. Our formulation is theoretically justified, yet remains practical, requiring only minimal modifications to standard velocity-driven models. We implement this through a scalable, neural network-based training objective. Experiments on synthetic, image, and biological datasets demonstrate that our method recovers hierarchy-aware structures, improves distributional metrics over strong flow-based baselines, and reaches targets in fewer steps.

We present MeshFlow, a new method for generating artist-like 3D meshes. Current mesh generators often adopt Auto-Regressive (AR) next-token prediction, a natural choice given the discrete nature of mesh topology. However, AR methods scale poorly because the inference cost is quadratic in mesh size. They also require discretizing the vertex coordinates, which introduces quantization errors. To address these challenges, we introduce a Variational Autoencoder (VAE) that, supervised with a contrastive loss, represents both continuous vertex positions and discrete connectivity in a continuous latent space. This latent space is significantly more compact than prior token-based mesh representations. We then build a 3D generator based on a Rectified Flow transformer, generating all mesh vertices and edges in parallel. Our model generates meshes 18x faster than the fastest AR generator while also achieving excellent accuracy across standard mesh-generation metrics. Homepage: https://mesh-flow.github.io/, Code: https://github.com/facebookresearch/meshflow

We introduce COT-FM, a general framework that reshapes the probability path in Flow Matching (FM) to achieve faster and more reliable generation. FM models often produce curved trajectories due to random or batchwise couplings, which increase discretization error and reduce sample quality. COT-FM fixes this by clustering target samples and assigning each cluster a dedicated source distribution obtained by reversing pretrained FM models. This divide-and-conquer strategy yields more accurate local transport and significantly straighter vector fields, all without changing the model architecture. As a plug-and-play approach, COT-FM consistently accelerates sampling and improves generation quality across 2D datasets, image generation benchmarks, and robotic manipulation tasks.

Recently, there has been tremendous progress in visual synthesis and the underlying generative models. Here, diffusion models (DMs) stand out particularly, but lately, flow matching (FM) has also garnered considerable interest. While DMs excel in providing diverse images, they suffer from long training and slow generation. With latent diffusion, these issues are only partially alleviated. Conversely, FM offers faster training and inference but exhibits less diversity in synthesis. We demonstrate that introducing FM between the Diffusion model and the convolutional decoder offers high-resolution image synthesis with reduced computational cost and model size. Diffusion can then efficiently provide the necessary generation diversity. FM compensates for the lower resolution, mapping the small latent space to a high-dimensional one. Subsequently, the convolutional decoder of the LDM maps these latents to high-resolution images. By combining the diversity of DMs, the efficiency of FMs, and the effectiveness of convolutional decoders, we achieve state-of-the-art high-resolution image synthesis at 1024^2 with minimal computational cost. Importantly, our approach is orthogonal to recent approximation and speed-up strategies for the underlying DMs, making it easily integrable into various DM frameworks.

Flow matching over carefully designed latent representations has recently emerged as a powerful paradigm for topology-aware mesh generation. Existing approaches, however, model vertices and connectivity jointly in a joint latent space, entangling continuous vertex geometry with discrete combinatorial structure; this complicates flow learning and manifests as drifting vertices and broken surfaces. We present LATO.2, a factorized flow matching framework that decomposes mesh generation into a vertex flow followed by a connectivity flow conditioned on the realized vertices, with both stages anchored to a shared coarse voxel scaffold. Dedicated VAEs underpin the two stages, recovering vertices at sub-voxel precision and embedding discrete connectivity into a continuous latent space. We demonstrate two advantages unique to this factorization: (i) part-wise generation, in which the scaffold is partitioned and each part synthesized at full latent capacity, yielding substantially higher-resolution meshes than a monolithic latent permits; and (ii) topology-adaptive editing, in which manipulating first-stage vertices induces the corresponding connectivity without re-optimization. Experiments show that LATO.2 surpasses state-of-the-art topology-aware mesh generators in geometric fidelity and connectivity quality.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Flow Matching has emerged as a powerful framework for learning continuous transformations between distributions, enabling high-fidelity generative modeling. This work introduces Symmetrical Flow Matching (SymmFlow), a new formulation that unifies semantic segmentation, classification, and image generation within a single model. Using a symmetric learning objective, SymmFlow models forward and reverse transformations jointly, ensuring bi-directional consistency, while preserving sufficient entropy for generative diversity. A new training objective is introduced to explicitly retain semantic information across flows, featuring efficient sampling while preserving semantic structure, allowing for one-step segmentation and classification without iterative refinement. Unlike previous approaches that impose strict one-to-one mapping between masks and images, SymmFlow generalizes to flexible conditioning, supporting both pixel-level and image-level class labels. Experimental results on various benchmarks demonstrate that SymmFlow achieves state-of-the-art performance on semantic image synthesis, obtaining FID scores of 11.9 on CelebAMask-HQ and 7.0 on COCO-Stuff with only 25 inference steps. Additionally, it delivers competitive results on semantic segmentation and shows promising capabilities in classification tasks. The code will be publicly available.

Conventional physically based rendering (PBR) pipelines generate photorealistic images through computationally intensive light transport simulations. Although recent deep learning approaches leverage diffusion model priors with geometry buffers (G-buffers) to produce visually compelling results without explicit scene geometry or light simulation, they remain constrained by two major limitations. First, the iterative nature of the diffusion process introduces substantial latency. Second, the inherent stochasticity of these generative models compromises physical accuracy and temporal consistency. In response to these challenges, we propose a novel, end-to-end, deterministic, single-step neural rendering framework, RenderFlow, built upon a flow matching paradigm. To further strengthen both rendering quality and generalization, we propose an efficient and effective module for sparse keyframe guidance. Our method significantly accelerates the rendering process and, by optionally incorporating sparsely rendered keyframes as guidance, enhances both the physical plausibility and overall visual quality of the output. The resulting pipeline achieves near real-time performance with photorealistic rendering quality, effectively bridging the gap between the efficiency of modern generative models and the precision of traditional physically based rendering. Furthermore, we demonstrate the versatility of our framework by introducing a lightweight, adapter-based module that efficiently repurposes the pretrained forward model for the inverse rendering task of intrinsic decomposition.

Diffusion- and flow-based models have emerged as state-of-the-art generative modeling approaches, but they require many sampling steps. Consistency models can distill these models into efficient one-step generators; however, unlike flow- and diffusion-based methods, their performance inevitably degrades when increasing the number of steps, which we show both analytically and empirically. Flow maps generalize these approaches by connecting any two noise levels in a single step and remain effective across all step counts. In this paper, we introduce two new continuous-time objectives for training flow maps, along with additional novel training techniques, generalizing existing consistency and flow matching objectives. We further demonstrate that autoguidance can improve performance, using a low-quality model for guidance during distillation, and an additional boost can be achieved by adversarial finetuning, with minimal loss in sample diversity. We extensively validate our flow map models, called Align Your Flow, on challenging image generation benchmarks and achieve state-of-the-art few-step generation performance on both ImageNet 64x64 and 512x512, using small and efficient neural networks. Finally, we show text-to-image flow map models that outperform all existing non-adversarially trained few-step samplers in text-conditioned synthesis.

We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models. We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples. Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences. We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.

Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design choice is the shape representation. An effective shape representation needs to adhere three design principles: it should allow an efficient conversion of large 3D datasets to the representation form; it should provide a good tradeoff of approximation power versus number of parameters; and it should have a simple tensorial form that is compatible with existing powerful neural architectures. While standard 3D shape representations such as volumetric grids and point clouds do not adhere to all these principles simultaneously, we advocate in this paper a new representation that does. We introduce Mosaic-SDF (M-SDF): a simple 3D shape representation that approximates the Signed Distance Function (SDF) of a given shape by using a set of local grids spread near the shape's boundary. The M-SDF representation is fast to compute for each shape individually making it readily parallelizable; it is parameter efficient as it only covers the space around the shape's boundary; and it has a simple matrix form, compatible with Transformer-based architectures. We demonstrate the efficacy of the M-SDF representation by using it to train a 3D generative flow model including class-conditioned generation with the 3D Warehouse dataset, and text-to-3D generation using a dataset of about 600k caption-shape pairs.

Conditional generative modeling aims to learn a conditional data distribution from samples containing data-condition pairs. For this, diffusion and flow-based methods have attained compelling results. These methods use a learned (flow) model to transport an initial standard Gaussian noise that ignores the condition to the conditional data distribution. The model is hence required to learn both mass transport and conditional injection. To ease the demand on the model, we propose Condition-Aware Reparameterization for Flow Matching (CAR-Flow) -- a lightweight, learned shift that conditions the source, the target, or both distributions. By relocating these distributions, CAR-Flow shortens the probability path the model must learn, leading to faster training in practice. On low-dimensional synthetic data, we visualize and quantify the effects of CAR. On higher-dimensional natural image data (ImageNet-256), equipping SiT-XL/2 with CAR-Flow reduces FID from 2.07 to 1.68, while introducing less than 0.6% additional parameters.

We propose Terminal Velocity Matching (TVM), a generalization of flow matching that enables high-fidelity one- and few-step generative modeling. TVM models the transition between any two diffusion timesteps and regularizes its behavior at its terminal time rather than at the initial time. We prove that TVM provides an upper bound on the 2-Wasserstein distance between data and model distributions when the model is Lipschitz continuous. However, since Diffusion Transformers lack this property, we introduce minimal architectural changes that achieve stable, single-stage training. To make TVM efficient in practice, we develop a fused attention kernel that supports backward passes on Jacobian-Vector Products, which scale well with transformer architectures. On ImageNet-256x256, TVM achieves 3.29 FID with a single function evaluation (NFE) and 1.99 FID with 4 NFEs. It similarly achieves 4.32 1-NFE FID and 2.94 4-NFE FID on ImageNet-512x512, representing state-of-the-art performance for one/few-step models from scratch.

Existing 3D editing methods rely on computationally intensive scene-by-scene iterative optimization and suffer from multi-view inconsistency. We propose an effective and feed-forward 3D editing framework based on the TRELLIS generative backbone, capable of modifying 3D models from a single editing view. Our framework addresses two key issues: adapting training-free 2D editing to structured 3D representations, and overcoming the bottleneck of appearance fidelity in compressed 3D features. To ensure geometric consistency, we introduce Voxel FlowEdit, an edit-driven flow in the sparse voxel latent space that achieves globally consistent 3D deformation in a single pass. To restore high-fidelity details, we develop a normal-guided single to multi-view generation module as an external appearance prior, successfully recovering high-frequency textures. Experiments demonstrate that our method enables fast, globally consistent, and high-fidelity 3D model editing.

Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into a straight line for a few-step and even one-step generation. However, in this paper, we suggest that the original training pipeline of flow matching is not optimal and introduce two techniques to improve it. Firstly, we introduce progressive reflow, which progressively reflows the diffusion models in local timesteps until the whole diffusion progresses, reducing the difficulty of flow matching. Second, we introduce aligned v-prediction, which highlights the importance of direction matching in flow matching over magnitude matching. Experimental results on SDv1.5 and SDXL demonstrate the effectiveness of our method, for example, conducting on SDv1.5 achieves an FID of 10.70 on MSCOCO2014 validation set with only 4 sampling steps, close to our teacher model (32 DDIM steps, FID = 10.05).

Current feed-forward 3D/4D reconstruction systems rely on dense geometry and pose supervision -- expensive to obtain at scale and particularly scarce for dynamic real-world scenes. We present Flow3r, a framework that augments visual geometry learning with dense 2D correspondences (`flow') as supervision, enabling scalable training from unlabeled monocular videos. Our key insight is that the flow prediction module should be factored: predicting flow between two images using geometry latents from one and pose latents from the other. This factorization directly guides the learning of both scene geometry and camera motion, and naturally extends to dynamic scenes. In controlled experiments, we show that factored flow prediction outperforms alternative designs and that performance scales consistently with unlabeled data. Integrating factored flow into existing visual geometry architectures and training with {sim}800K unlabeled videos, Flow3r achieves state-of-the-art results across eight benchmarks spanning static and dynamic scenes, with its largest gains on in-the-wild dynamic videos where labeled data is most scarce.

Advanced generative models excel at synthesizing images but often rely on text-based conditioning. Visual designers, however, often work beyond language, directly drawing inspiration from existing visual elements. In many cases, these elements represent only fragments of a potential concept-such as an uniquely structured wing, or a specific hairstyle-serving as inspiration for the artist to explore how they can come together creatively into a coherent whole. Recognizing this need, we introduce a generative framework that seamlessly integrates a partial set of user-provided visual components into a coherent composition while simultaneously sampling the missing parts needed to generate a plausible and complete concept. Our approach builds on a strong and underexplored representation space, extracted from IP-Adapter+, on which we train IP-Prior, a lightweight flow-matching model that synthesizes coherent compositions based on domain-specific priors, enabling diverse and context-aware generations. Additionally, we present a LoRA-based fine-tuning strategy that significantly improves prompt adherence in IP-Adapter+ for a given task, addressing its common trade-off between reconstruction quality and prompt adherence.

We present Seen2Scene, the first flow matching-based approach that trains directly on incomplete, real-world 3D scans for scene completion and generation. Unlike prior methods that rely on complete and hence synthetic 3D data, our approach introduces visibility-guided flow matching, which explicitly masks out unknown regions in real scans, enabling effective learning from real-world, partial observations. We represent 3D scenes using truncated signed distance field (TSDF) volumes encoded in sparse grids and employ a sparse transformer to efficiently model complex scene structures while masking unknown regions. We employ 3D layout boxes as an input conditioning signal, and our approach is flexibly adapted to various other inputs such as text or partial scans. By learning directly from real-world, incomplete 3D scans, Seen2Scene enables realistic 3D scene completion for complex, cluttered real environments. Experiments demonstrate that our model produces coherent, complete, and realistic 3D scenes, outperforming baselines in completion accuracy and generation quality.

Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards the conditional velocity field. However, on constrained domains, the learned velocity model may lead to undesirable flows that result in highly unnatural samples, e.g., oversaturated images, due to both flow matching error and simulation error. To address this, we add a boundary constraint term to CNFs, which leads to reflected CNFs that keep trajectories within the constrained domains. We propose reflected flow matching (RFM) to train the velocity model in reflected CNFs by matching the conditional velocity fields in a simulation-free manner, similar to the vanilla FM. Moreover, the analytical form of conditional velocity fields in RFM avoids potentially biased approximations, making it superior to existing score-based generative models on constrained domains. We demonstrate that RFM achieves comparable or better results on standard image benchmarks and produces high-quality class-conditioned samples under high guidance weight.

Taming diffusion models for generative segmentation has attracted increasing attention. While existing approaches primarily focus on architectural tweaks or training heuristics, there remains a limited understanding of the intrinsic mismatch between continuous flow matching objectives and discrete perception tasks. In this work, we revisit diffusion segmentation from the perspective of vector field learning. We identify two key limitations of the commonly used flow matching objective: gradient vanishing and trajectory traversing, which result in slow convergence and poor class separation. To tackle these issues, we propose a principled vector field reshaping strategy that augments the learned velocity field with a detached distance-aware correction term. This correction introduces both attractive and repulsive interactions, enhancing gradient magnitudes near centroids while preserving the original diffusion training framework. Furthermore, we design a computationally efficient, quasi-random category encoding scheme inspired by Kronecker sequences, which integrates seamlessly with an end-to-end pixel neural field framework for pixel-level semantic alignment. Extensive experiments consistently demonstrate significant improvements over vanilla flow matching approaches, substantially narrowing the performance gap between generative segmentation and strong discriminative specialists.

Flow Matching models have demonstrated strong performance across a wide range of generative tasks. However, their reliance on ODE-based iterative sampling incurs substantial computational overhead in inference, which limits their applicability in real-time scenes. While distillation is a promising solution, existing approaches largely borrow from diffusion-based score matching, often failing to exploit the intrinsic geometric structure of flows and suffering from training instability, high variance, and degraded generation quality. In this paper, we propose Mean Flow Distillation (MFD), a novel distillation framework tailored for flow matching models. We theoretically demonstrate that MFD acts as a temporal low-pass filter, effectively suppressing the high-frequency optimization noise inherent in variational score distillation (VSD) while ensuring global trajectory consistency. We further prove the Mean Flow Matching Theorem, establishing that matching expected average velocities is sufficient for strict distribution alignment. Empirically, on challenging tasks of high-dimensional manifolds including 4D occupancy forecasting and text-to-image generation, MFD achieves state-of-the-art performance, enabling high-fidelity single-step generation.

Recent advancements in generative models have unlocked the capabilities to render photo-realistic data in a controllable fashion. Trained on the real data, these generative models are capable of producing realistic samples with minimal to no domain gap, as compared to the traditional graphics rendering. However, using the data generated using such models for training downstream tasks remains under-explored, mainly due to the lack of 3D consistent annotations. Moreover, controllable generative models are learned from massive data and their latent space is often too vast to obtain meaningful sample distributions for downstream task with limited generation. To overcome these challenges, we extract 3D consistent annotations from an existing controllable generative model, making the data useful for downstream tasks. Our experiments show competitive performance against state-of-the-art models using only generated synthetic data, demonstrating potential for solving downstream tasks. Project page: https://synth-forge.github.io

Video generation requires modeling a vast spatiotemporal space, which demands significant computational resources and data usage. To reduce the complexity, the prevailing approaches employ a cascaded architecture to avoid direct training with full resolution. Despite reducing computational demands, the separate optimization of each sub-stage hinders knowledge sharing and sacrifices flexibility. This work introduces a unified pyramidal flow matching algorithm. It reinterprets the original denoising trajectory as a series of pyramid stages, where only the final stage operates at the full resolution, thereby enabling more efficient video generative modeling. Through our sophisticated design, the flows of different pyramid stages can be interlinked to maintain continuity. Moreover, we craft autoregressive video generation with a temporal pyramid to compress the full-resolution history. The entire framework can be optimized in an end-to-end manner and with a single unified Diffusion Transformer (DiT). Extensive experiments demonstrate that our method supports generating high-quality 5-second (up to 10-second) videos at 768p resolution and 24 FPS within 20.7k A100 GPU training hours. All code and models will be open-sourced at https://pyramid-flow.github.io.

This report presents a comprehensive framework for generating high-quality 3D shapes and textures from diverse input prompts, including single images, multi-view images, and text descriptions. The framework consists of 3D shape generation and texture generation. (1). The 3D shape generation pipeline employs a Variational Autoencoder (VAE) to encode implicit 3D geometries into a latent space and a diffusion network to generate latents conditioned on input prompts, with modifications to enhance model capacity. An alternative Artist-Created Mesh (AM) generation approach is also explored, yielding promising results for simpler geometries. (2). Texture generation involves a multi-stage process starting with frontal images generation followed by multi-view images generation, RGB-to-PBR texture conversion, and high-resolution multi-view texture refinement. A consistency scheduler is plugged into every stage, to enforce pixel-wise consistency among multi-view textures during inference, ensuring seamless integration. The pipeline demonstrates effective handling of diverse input formats, leveraging advanced neural architectures and novel methodologies to produce high-quality 3D content. This report details the system architecture, experimental results, and potential future directions to improve and expand the framework. The source code and pretrained weights are released at: https://github.com/Tencent/Tencent-XR-3DGen.

3D shape modeling is labor-intensive, time-consuming, and requires years of expertise. To facilitate 3D shape modeling, we propose a 3D shape generation network that takes a 3D VR sketch as a condition. We assume that sketches are created by novices without art training and aim to reconstruct geometrically realistic 3D shapes of a given category. To handle potential sketch ambiguity, our method creates multiple 3D shapes that align with the original sketch's structure. We carefully design our method, training the model step-by-step and leveraging multi-modal 3D shape representation to support training with limited training data. To guarantee the realism of generated 3D shapes we leverage the normalizing flow that models the distribution of the latent space of 3D shapes. To encourage the fidelity of the generated 3D shapes to an input sketch, we propose a dedicated loss that we deploy at different stages of the training process. The code is available at https://github.com/Rowl1ng/3Dsketch2shape.

In the past, normalizing generative flows have emerged as a promising class of generative models for natural images. This type of model has many modeling advantages: the ability to efficiently compute log-likelihood of the input data, fast generation and simple overall structure. Normalizing flows remained a topic of active research but later fell out of favor, as visual quality of the samples was not competitive with other model classes, such as GANs, VQ-VAE-based approaches or diffusion models. In this paper we revisit the design of the coupling-based normalizing flow models by carefully ablating prior design choices and using computational blocks based on the Vision Transformer architecture, not convolutional neural networks. As a result, we achieve state-of-the-art quantitative and qualitative performance with a much simpler architecture. While the overall visual quality is still behind the current state-of-the-art models, we argue that strong normalizing flow models can help advancing research frontier by serving as building components of more powerful generative models.

Generating 3D models lies at the core of computer graphics and has been the focus of decades of research. With the emergence of advanced neural representations and generative models, the field of 3D content generation is developing rapidly, enabling the creation of increasingly high-quality and diverse 3D models. The rapid growth of this field makes it difficult to stay abreast of all recent developments. In this survey, we aim to introduce the fundamental methodologies of 3D generation methods and establish a structured roadmap, encompassing 3D representation, generation methods, datasets, and corresponding applications. Specifically, we introduce the 3D representations that serve as the backbone for 3D generation. Furthermore, we provide a comprehensive overview of the rapidly growing literature on generation methods, categorized by the type of algorithmic paradigms, including feedforward generation, optimization-based generation, procedural generation, and generative novel view synthesis. Lastly, we discuss available datasets, applications, and open challenges. We hope this survey will help readers explore this exciting topic and foster further advancements in the field of 3D content generation.

Modern image generation demands a single model that unifies diverse capabilities, including text-to-image (T2I), local editing, and global editing. However, these capabilities are rarely naturally aligned and often conflict. For instance, editing tends to degrade T2I performance, while global and local editing interfere with each other. Consequently, effectively composing these capabilities has become a central challenge for image generation model training. To tackle this, we introduce DanceOPD, an on-policy generative field distillation framework for flow-matching models that routes each sample to one capability field, queries one low-noise student-induced state, and trains with a simple velocity MSE objective. With each capability source defined as a velocity field over the shared flow state space, the student learns from fields queried on its own rollout states to compose expert capabilities. This formulation also absorbs operator-defined fields such as classifier-free guidance. Comprehensive experiments on T2I, editing, realism-field absorption, and CFG absorption show that our approach improves multi-capability composition, strengthening target capabilities while preserving anchor generation quality. We believe this work establishes a practical route for generative field distillation in flow-matching models.

Detector simulations are an exciting application of modern generative networks. Their sparse high-dimensional data combined with the required precision poses a serious challenge. We show how combining Conditional Flow Matching with transformer elements allows us to simulate the detector phase space reliably. Namely, we use an autoregressive transformer to simulate the energy of each layer, and a vision transformer for the high-dimensional voxel distributions. We show how dimension reduction via latent diffusion allows us to train more efficiently and how diffusion networks can be evaluated faster with bespoke solvers. We showcase our framework, CaloDREAM, on datasets 2 and 3 of the CaloChallenge.

Diffusion and flow-based models have become the state of the art for generative AI across a wide range of data modalities, including images, videos, shapes, molecules, music, and more. This tutorial provides a self-contained introduction to diffusion and flow-based generative models from first principles. We systematically develop the necessary mathematical background in ordinary and stochastic differential equations and derive the core algorithms of flow matching and denoising diffusion models. We then provide a step-by-step guide to building image and video generators, including training methods, guidance, and architectural design. This course is ideal for machine learning researchers who want to develop a principled understanding of the theory and practice of generative AI.

Deep generative models of 3D shapes have received a great deal of research interest. Yet, almost all of them generate discrete shape representations, such as voxels, point clouds, and polygon meshes. We present the first 3D generative model for a drastically different shape representation --- describing a shape as a sequence of computer-aided design (CAD) operations. Unlike meshes and point clouds, CAD models encode the user creation process of 3D shapes, widely used in numerous industrial and engineering design tasks. However, the sequential and irregular structure of CAD operations poses significant challenges for existing 3D generative models. Drawing an analogy between CAD operations and natural language, we propose a CAD generative network based on the Transformer. We demonstrate the performance of our model for both shape autoencoding and random shape generation. To train our network, we create a new CAD dataset consisting of 178,238 models and their CAD construction sequences. We have made this dataset publicly available to promote future research on this topic.

Flow matching has emerged as a compelling generative modeling approach that is widely used across domains. To generate data via a flow matching model, an ordinary differential equation (ODE) is numerically solved via forward integration of the modeled velocity field. To better capture the multi-modality that is inherent in typical velocity fields, hierarchical flow matching was recently introduced. It uses a hierarchy of ODEs that are numerically integrated when generating data. This hierarchy of ODEs captures the multi-modal velocity distribution just like vanilla flow matching is capable of modeling a multi-modal data distribution. While this hierarchy enables to model multi-modal velocity distributions, the complexity of the modeled distribution remains identical across levels of the hierarchy. In this paper, we study how to gradually adjust the complexity of the distributions across different levels of the hierarchy via mini-batch couplings. We show the benefits of mini-batch couplings in hierarchical rectified flow matching via compelling results on synthetic and imaging data. Code is available at https://riccizz.github.io/HRF_coupling.

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

Recent advancements in diffusion techniques have propelled image and video generation to unprece- dented levels of quality, significantly accelerating the deployment and application of generative AI. However, 3D shape generation technology has so far lagged behind, constrained by limitations in 3D data scale, complexity of 3D data process- ing, and insufficient exploration of advanced tech- niques in the 3D domain. Current approaches to 3D shape generation face substantial challenges in terms of output quality, generalization capa- bility, and alignment with input conditions. We present TripoSG, a new streamlined shape diffu- sion paradigm capable of generating high-fidelity 3D meshes with precise correspondence to input images. Specifically, we propose: 1) A large-scale rectified flow transformer for 3D shape generation, achieving state-of-the-art fidelity through training on extensive, high-quality data. 2) A hybrid supervised training strategy combining SDF, normal, and eikonal losses for 3D VAE, achieving high- quality 3D reconstruction performance. 3) A data processing pipeline to generate 2 million high- quality 3D samples, highlighting the crucial rules for data quality and quantity in training 3D gen- erative models. Through comprehensive experi- ments, we have validated the effectiveness of each component in our new framework. The seamless integration of these parts has enabled TripoSG to achieve state-of-the-art performance in 3D shape generation. The resulting 3D shapes exhibit en- hanced detail due to high-resolution capabilities and demonstrate exceptional fidelity to input im- ages. Moreover, TripoSG demonstrates improved versatility in generating 3D models from diverse image styles and contents, showcasing strong gen- eralization capabilities. To foster progress and innovation in the field of 3D generation, we will make our model publicly available.

Strong semantic representations improve the convergence and generation quality of diffusion and flow models. Existing approaches largely rely on external models, which require separate training, operate on misaligned objectives, and exhibit unexpected scaling behavior. We argue that this dependence arises from the model's training objective, which poses a denoising task with little incentive to learn semantic representations. We introduce Self-Flow: a self-supervised flow matching paradigm that integrates representation learning within the generative framework. Our key mechanism, Dual-Timestep Scheduling, applies heterogeneous noise levels across tokens, creating an information asymmetry that forces the model to infer missing information from corrupted inputs. This drives learning strong representations alongside generative capabilities without external supervision. Our method generalizes across modalities and enables multi-modal training while following expected scaling laws, achieving superior image, video, and audio generation.

We present adversarial flow models, a class of generative models that unifies adversarial models and flow models. Our method supports native one-step or multi-step generation and is trained using the adversarial objective. Unlike traditional GANs, where the generator learns an arbitrary transport plan between the noise and the data distributions, our generator learns a deterministic noise-to-data mapping, which is the same optimal transport as in flow-matching models. This significantly stabilizes adversarial training. Also, unlike consistency-based methods, our model directly learns one-step or few-step generation without needing to learn the intermediate timesteps of the probability flow for propagation. This saves model capacity, reduces training iterations, and avoids error accumulation. Under the same 1NFE setting on ImageNet-256px, our B/2 model approaches the performance of consistency-based XL/2 models, while our XL/2 model creates a new best FID of 2.38. We additionally show the possibility of end-to-end training of 56-layer and 112-layer models through depth repetition without any intermediate supervision, and achieve FIDs of 2.08 and 1.94 using a single forward pass, surpassing their 2NFE and 4NFE counterparts.

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely on a standard Gaussian distribution, a choice inherited from diffusion models, and rarely consider the source distribution itself as an optimization target in such settings. In this work, we show that principled design of the source distribution is not only feasible but also beneficial at the scale of modern text-to-image systems. Specifically, we propose learning a condition-dependent source distribution under flow matching objective that better exploit rich conditioning signals. We identify key failure modes that arise when directly incorporating conditioning into the source, including distributional collapse and instability, and show that appropriate variance regularization and directional alignment between source and target are critical for stable and effective learning. We further analyze how the choice of target representation space impacts flow matching with structured sources, revealing regimes in which such designs are most effective. Extensive experiments across multiple text-to-image benchmarks demonstrate consistent and robust improvements, including up to a 3x faster convergence in FID, highlighting the practical benefits of a principled source distribution design for conditional flow matching.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

Flow matching retains the generation quality of diffusion models while enabling substantially faster inference, making it a compelling paradigm for generative modeling. However, when applied to language modeling, it exhibits fundamental limitations in representing complex latent distributions with irregular geometries, such as anisotropy and multimodality. To address these challenges, we propose a mixture-of-experts flow matching (MoE-FM) framework, which captures complex global transport geometries in latent space by decomposing them into locally specialized vector fields. Building on MoE-FM, we develop a non-autoregressive (NAR) language modeling approach, named YAN, instantiated with both Transformer and Mamba architectures. Across multiple downstream tasks, YAN achieves generation quality on par with both autoregressive (AR) and diffusion-based NAR language models, while requiring as few as three sampling steps. This yields a 40times speedup over AR baselines and up to a 10^3times speedup over diffusion language models, demonstrating substantial efficiency advantages for language modeling.

Flow matching with x-prediction -- regressing the clean data point rather than the ambient velocity -- is known to exploit low-dimensional manifold structure effectively in pixel space li2025back. We ask whether a pretrained representation space, while containing a low-dimensional data manifold of comparable intrinsic dimensionality, offers a distribution more favorable for flow-matching learning. Comparing pixel, SD-VAE, and DINOv2 features along four geometric axes, we find that pixel and DINOv2 share nearly identical intrinsic dimensionalities (both d!approx!33) yet DINOv2 exhibits 7.3times higher effective rank, 35times better covariance conditioning, 11.5times lower excess kurtosis, and 1.7times lower on-manifold interpolation error; SD-VAE latents are consistently intermediate, indicating that the advantage stems from representation-learning objectives rather than mere compression. These statistical properties render the flow-matching regression well-conditioned and remove the need for the specialized prediction heads or Riemannian transport used by prior DINOv2 diffusion methods. We propose the Representation Image Transformer (RiT): a vanilla Diffusion Transformer trained by x-prediction on frozen DINOv2 features, augmented only by a dimension-aware noise schedule and joint [CLS]-patch modeling. On ImageNet 256{times}256, RiT attains FID 1.45 without guidance and 1.14 with classifier-free guidance, outperforming DiT^DH-XL with 19% fewer parameters (676M vs.\ 839M). The resulting ODE is efficiently solvable at coarse discretizations: with classifier-free guidance, 5 Heun steps already reach FID 2.0 and 10 steps reach 1.25, without distillation or consistency training. Code at https://github.com/lezhang7/RiT.

This paper presents a novel paradigm for building scalable 3D generative models utilizing pre-trained video diffusion models. The primary obstacle in developing foundation 3D generative models is the limited availability of 3D data. Unlike images, texts, or videos, 3D data are not readily accessible and are difficult to acquire. This results in a significant disparity in scale compared to the vast quantities of other types of data. To address this issue, we propose using a video diffusion model, trained with extensive volumes of text, images, and videos, as a knowledge source for 3D data. By unlocking its multi-view generative capabilities through fine-tuning, we generate a large-scale synthetic multi-view dataset to train a feed-forward 3D generative model. The proposed model, VFusion3D, trained on nearly 3M synthetic multi-view data, can generate a 3D asset from a single image in seconds and achieves superior performance when compared to current SOTA feed-forward 3D generative models, with users preferring our results over 70% of the time.

Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation enables the use of advanced numerical solvers to accelerate sampling. Orthogonal yet vital to solver design is the discretization strategy. While early approaches employed handcrafted heuristics and recent methods adopt optimization-based techniques, most existing strategies enforce a globally shared timestep schedule across all samples. This uniform treatment fails to account for instance-specific complexity in the generative process, potentially limiting performance. Motivated by controlled experiments on synthetic data, which reveals the suboptimality of global schedules under instance-specific dynamics, we propose an instance-aware discretization framework. Our method learns to adapt timestep allocations based on input-dependent priors, extending gradient-based discretization search to the conditional generative setting. Empirical results across diverse settings, including synthetic data, pixel-space diffusion, latent-space images and video flow matching models, demonstrate that our method consistently improves generation quality with marginal tuning cost compared to training and negligible inference overhead.

We describe Generative Blocks World to interact with the scene of a generated image by manipulating simple geometric abstractions. Our method represents scenes as assemblies of convex 3D primitives, and the same scene can be represented by different numbers of primitives, allowing an editor to move either whole structures or small details. Once the scene geometry has been edited, the image is generated by a flow-based method which is conditioned on depth and a texture hint. Our texture hint takes into account the modified 3D primitives, exceeding texture-consistency provided by existing key-value caching techniques. These texture hints (a) allow accurate object and camera moves and (b) largely preserve the identity of objects depicted. Quantitative and qualitative experiments demonstrate that our approach outperforms prior works in visual fidelity, editability, and compositional generalization.

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the Flux Matching objective imposes a weaker condition that admits infinitely many vector fields whose stationary distribution is the data. This flexibility enables a class of generative models that cannot be learned under score matching, in which inductive biases, structural priors, and properties of the dynamics can be directly imposed or optimized. We show that Flux Matching performs strongly on high-dimensional image datasets and, more importantly, that our added freedom unlocks a range of applications including faster sampling, interpretable and mechanistic models, and dynamics that encode directed dependencies between variables. More broadly, Flux Matching opens a new dimension in generative modeling by turning the vector field itself into a design choice rather than a fixed target. Code is available at https://github.com/peterpaohuang/flux_matching.

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing boldsymbol v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

MeanFlow has recently emerged as a powerful framework for few-step generative modeling trained from scratch, but its success is not yet fully understood. In this work, we show that the MeanFlow objective naturally decomposes into two parts: trajectory flow matching and trajectory consistency. Through gradient analysis, we find that these terms are strongly negatively correlated, causing optimization conflict and slow convergence. Motivated by these insights, we introduce alpha-Flow, a broad family of objectives that unifies trajectory flow matching, Shortcut Model, and MeanFlow under one formulation. By adopting a curriculum strategy that smoothly anneals from trajectory flow matching to MeanFlow, alpha-Flow disentangles the conflicting objectives, and achieves better convergence. When trained from scratch on class-conditional ImageNet-1K 256x256 with vanilla DiT backbones, alpha-Flow consistently outperforms MeanFlow across scales and settings. Our largest alpha-Flow-XL/2+ model achieves new state-of-the-art results using vanilla DiT backbones, with FID scores of 2.58 (1-NFE) and 2.15 (2-NFE).

Generating high-quality 3D assets from text and images has long been challenging, primarily due to the absence of scalable 3D representations capable of capturing intricate geometry distributions. In this work, we introduce Direct3D, a native 3D generative model scalable to in-the-wild input images, without requiring a multiview diffusion model or SDS optimization. Our approach comprises two primary components: a Direct 3D Variational Auto-Encoder (D3D-VAE) and a Direct 3D Diffusion Transformer (D3D-DiT). D3D-VAE efficiently encodes high-resolution 3D shapes into a compact and continuous latent triplane space. Notably, our method directly supervises the decoded geometry using a semi-continuous surface sampling strategy, diverging from previous methods relying on rendered images as supervision signals. D3D-DiT models the distribution of encoded 3D latents and is specifically designed to fuse positional information from the three feature maps of the triplane latent, enabling a native 3D generative model scalable to large-scale 3D datasets. Additionally, we introduce an innovative image-to-3D generation pipeline incorporating semantic and pixel-level image conditions, allowing the model to produce 3D shapes consistent with the provided conditional image input. Extensive experiments demonstrate the superiority of our large-scale pre-trained Direct3D over previous image-to-3D approaches, achieving significantly better generation quality and generalization ability, thus establishing a new state-of-the-art for 3D content creation. Project page: https://nju-3dv.github.io/projects/Direct3D/.

De novo 3D molecule generation is a pivotal task in drug discovery. However, many recent geometric generative models struggle to produce high-quality 3D structures, even if they maintain 2D validity and topological stability. To tackle this issue and enhance the learning of effective molecular generation dynamics, we present Megalodon-a family of scalable transformer models. These models are enhanced with basic equivariant layers and trained using a joint continuous and discrete denoising co-design objective. We assess Megalodon's performance on established molecule generation benchmarks and introduce new 3D structure benchmarks that evaluate a model's capability to generate realistic molecular structures, particularly focusing on energetics. We show that Megalodon achieves state-of-the-art results in 3D molecule generation, conditional structure generation, and structure energy benchmarks using diffusion and flow matching. Furthermore, doubling the number of parameters in Megalodon to 40M significantly enhances its performance, generating up to 49x more valid large molecules and achieving energy levels that are 2-10x lower than those of the best prior generative models.

Flow-matching methods for 3D shape assembly learn point-wise velocity fields that transport parts toward assembled configurations, yet they receive no explicit guidance about which cross-part interactions should drive the motion. We introduce TORA, a topology-first representation alignment framework that distills relational structure from a frozen pretrained 3D encoder into the flow-matching backbone during training. We first realize this via simple instantiation, token-wise cosine matching, which injects the learned geometric descriptors from the teacher representation. We then extend to employ a Centered Kernel Alignment (CKA) loss to match the similarity structure between student and teacher representations for enhanced topological alignment. Through systematic probing of diverse 3D encoders, we show that geometry- and contact-centric teacher properties, not semantic classification ability, govern alignment effectiveness, and that alignment is most beneficial at later transformer layers where spatial structure naturally emerges. TORA introduces zero inference overhead while yielding two consistent benefits: faster convergence (up to 6.9times) and improved accuracy in-distribution, along with greater robustness under domain shift. Experiments on five benchmarks spanning geometric, semantic, and inter-object assembly demonstrate state-of-the-art performance, with particularly pronounced gains in zero-shot transfer to unseen real-world and synthetic datasets. Project page: https://nahyuklee.github.io/tora.

Flow matching (FM) trains a time-dependent vector field that transports samples from a simple prior to a complex data distribution. However, for high-dimensional images, each training sample supervises only a single trajectory and intermediate point, yielding an extremely sparse and high-variance training signal. This under-constrained supervision can cause flow collapse, where the learned dynamics memorize specific source-target pairings, mapping diverse inputs to overly similar outputs, failing to generalize. We introduce Posterior-Augmented Flow Matching (PAFM), a theoretically grounded generalization of FM that replaces single-target supervision with an expectation over an approximate posterior of valid target completions for a given intermediate state and condition. PAFM factorizes this intractable posterior into (i) the likelihood of the intermediate under a hypothesized endpoint and (ii) the prior probability of that endpoint under the condition, and uses an importance sampling scheme to construct a mixture over multiple candidate targets. We prove that PAFM yields an unbiased estimator of the original FM objective while substantially reducing gradient variance during training by aggregating information from many plausible continuation trajectories per intermediate. Finally, we show that PAFM improves over FM by up to 3.4 FID50K across different model scales (SiT-B/2 and SiT-XL/2), different architectures (SiT and MMDiT), and in both class and text conditioned benchmarks (ImageNet and CC12M), with a negligible increase in the compute overhead. Code: https://github.com/gstoica27/PAFM.git.

Autoregressive Transformers dominate high-quality mesh generation by producing artist-worthy topologies, yet their inherent sequential decoding induces substantial computational overhead, falling orders of magnitude slower than parallel generative models. On the other hand, while continuous diffusion and flow-matching methods support efficient parallel synthesis across a variety of domains, they cannot be directly applied to meshes: mesh connectivity is inherently discrete and incompatible with standard continuous noise injection and denoising operations. To resolve this fundamental incompatibility, we introduce a compact topology embedder that projects discrete mesh vertex positions and normals into continuous per-vertex embeddings, where the original discrete adjacency information can be faithfully recovered via spacetime distance thresholding. After pretraining and freezing this embedder, any raw mesh can be fully converted into a continuous per-vertex state space unifying position, normal, and implicit topological attributes. Built upon this novel continuous mesh representation, we present PolyFlow, a Transformer-based flow-matching framework that achieves fully parallel vertex state denoising conditioned on extracted point-cloud features. During inference, our model completes generation rapidly via an ODE solver, and supports explicit, precise control over output mesh resolution by directly specifying the target vertex count. Extensive evaluations on the Toys4K benchmark demonstrate that PolyFlow surpasses state-of-the-art autoregressive baselines in both Chamfer Distance and Hausdorff Distance.

Finding a suitable layout represents a crucial task for diverse applications in graphic design. Motivated by simpler and smoother sampling trajectories, we explore the use of Flow Matching as an alternative to current diffusion-based layout generation models. Specifically, we propose LayoutFlow, an efficient flow-based model capable of generating high-quality layouts. Instead of progressively denoising the elements of a noisy layout, our method learns to gradually move, or flow, the elements of an initial sample until it reaches its final prediction. In addition, we employ a conditioning scheme that allows us to handle various generation tasks with varying degrees of conditioning with a single model. Empirically, LayoutFlow performs on par with state-of-the-art models while being significantly faster.

Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG). To address these limitations, we propose a novel Gaussian mixture flow matching (GMFlow) model: instead of predicting the mean, GMFlow predicts dynamic Gaussian mixture (GM) parameters to capture a multi-modal flow velocity distribution, which can be learned with a KL divergence loss. We demonstrate that GMFlow generalizes previous diffusion and flow matching models where a single Gaussian is learned with an L_2 denoising loss. For inference, we derive GM-SDE/ODE solvers that leverage analytic denoising distributions and velocity fields for precise few-step sampling. Furthermore, we introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality. Extensive experiments demonstrate that GMFlow consistently outperforms flow matching baselines in generation quality, achieving a Precision of 0.942 with only 6 sampling steps on ImageNet 256times256.

Monocular 3D pose estimation is fundamentally ill-posed due to depth ambiguity and occlusions, thereby motivating probabilistic methods that generate multiple plausible 3D pose hypotheses. In particular, diffusion-based models have recently demonstrated strong performance, but their iterative denoising process typically requires many timesteps for each prediction, making inference computationally expensive. In contrast, we leverage Flow Matching (FM) to learn a velocity field defined by an Ordinary Differential Equation (ODE), enabling efficient generation of 3D pose samples with only a few integration steps. We propose a novel generative pose estimation framework, FMPose3D, that formulates 3D pose estimation as a conditional distribution transport problem. It continuously transports samples from a standard Gaussian prior to the distribution of plausible 3D poses conditioned only on 2D inputs. Although ODE trajectories are deterministic, FMPose3D naturally generates various pose hypotheses by sampling different noise seeds. To obtain a single accurate prediction from those hypotheses, we further introduce a Reprojection-based Posterior Expectation Aggregation (RPEA) module, which approximates the Bayesian posterior expectation over 3D hypotheses. FMPose3D surpasses existing methods on the widely used human pose estimation benchmarks Human3.6M and MPI-INF-3DHP, and further achieves state-of-the-art performance on the 3D animal pose datasets Animal3D and CtrlAni3D, demonstrating strong performance across both 3D pose domains. The code is available at https://github.com/AdaptiveMotorControlLab/FMPose3D.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis. However, standard diffusion transformers fail to converge on these representations directly. While recent work attributes this to a capacity bottleneck proposing computationally expensive width scaling of diffusion transformers we demonstrate that the failure is fundamentally geometric. We identify Geometric Interference as the root cause: standard Euclidean flow matching forces probability paths through the low-density interior of the hyperspherical feature space of representation encoders, rather than following the manifold surface. To resolve this, we propose Riemannian Flow Matching with Jacobi Regularization (RJF). By constraining the generative process to the manifold geodesics and correcting for curvature-induced error propagation, RJF enables standard Diffusion Transformer architectures to converge without width scaling. Our method RJF enables the standard DiT-B architecture (131M parameters) to converge effectively, achieving an FID of 3.37 where prior methods fail to converge. Code: https://github.com/amandpkr/RJF

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.

In this work, we show that Latent Flow-Matching (LFM) models are robust to different types of perturbations, including data reduction and model capacity shrinkage. We characterize this stability by their tendency to generate similar outputs under identical noise seeds. We provide a perspective relating this phenomenon to flow matching theory, which indicates that this stability is inherent to the FM objective. We further exploit this stability to derive practical algorithms for more efficient training and inference. Concretely, first, we show that by training LFM models on significantly reduced datasets, the performance does not degrade perceptually or quantitatively. This yields multiple advantages, such as reducing training time by converging faster under limited compute budget, and alleviating annotation effort when training conditional models. Second, LFM stability under architectural shrinkage gives rise to a two-model coarse-to-fine approach, one using a light-weight architecture for the first phase of the FM trajectory, and one with higher capacity for the second, thereby reducing the inference cost substantially. To determine which samples are informative, we introduce three sample-scoring criteria and evaluate them under standard metrics for generative models. Our results are thoroughly evaluated on multiple datasets, demonstrating the practical advantage of this stability, including data saving and a more than two-fold inference speedup while generating comparable outputs.

World modeling requires forecasting uncertain futures while preserving information useful for downstream perception. Existing visual world models often struggle to satisfy both goals: VAE-based stochastic models operate in low-dimensional reconstruction latents, which can limit perception performance, while deterministic predictors using strong pretrained features collapse multimodal futures into a single blurry mean. In this work, we propose FlowWM, a stochastic world model that performs flow matching directly within pretrained feature space (e.g., DINOv3). This is challenging because pretrained features are substantially high-dimensional, making standard diffusion recipes suboptimal. To address this, we investigate the design choices needed for feature-space flow matching and introduce a differentiable one-step projection mechanism that enables efficient training with temporal consistency and task-driven objectives. We evaluate FlowWM on two benchmarks: a synthetic benchmark for systematic evaluation of accuracy and diversity, and a real-world benchmark FuturePerception. FlowWM improves perception performance, mode coverage, and horizon robustness, validating our proposed design for stochastic world modeling in high-dimensional feature spaces.

We present evaluation results for FLUX.1 Kontext, a generative flow matching model that unifies image generation and editing. The model generates novel output views by incorporating semantic context from text and image inputs. Using a simple sequence concatenation approach, FLUX.1 Kontext handles both local editing and generative in-context tasks within a single unified architecture. Compared to current editing models that exhibit degradation in character consistency and stability across multiple turns, we observe that FLUX.1 Kontext improved preservation of objects and characters, leading to greater robustness in iterative workflows. The model achieves competitive performance with current state-of-the-art systems while delivering significantly faster generation times, enabling interactive applications and rapid prototyping workflows. To validate these improvements, we introduce KontextBench, a comprehensive benchmark with 1026 image-prompt pairs covering five task categories: local editing, global editing, character reference, style reference and text editing. Detailed evaluations show the superior performance of FLUX.1 Kontext in terms of both single-turn quality and multi-turn consistency, setting new standards for unified image processing models.

The field of neural rendering has witnessed significant progress with advancements in generative models and differentiable rendering techniques. Though 2D diffusion has achieved success, a unified 3D diffusion pipeline remains unsettled. This paper introduces a novel framework called LN3Diff to address this gap and enable fast, high-quality, and generic conditional 3D generation. Our approach harnesses a 3D-aware architecture and variational autoencoder (VAE) to encode the input image into a structured, compact, and 3D latent space. The latent is decoded by a transformer-based decoder into a high-capacity 3D neural field. Through training a diffusion model on this 3D-aware latent space, our method achieves state-of-the-art performance on ShapeNet for 3D generation and demonstrates superior performance in monocular 3D reconstruction and conditional 3D generation across various datasets. Moreover, it surpasses existing 3D diffusion methods in terms of inference speed, requiring no per-instance optimization. Our proposed LN3Diff presents a significant advancement in 3D generative modeling and holds promise for various applications in 3D vision and graphics tasks.