Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
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Score-Based Generative Modeling through Stochastic Differential Equations
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abstract
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
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- abstract Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate
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representative citing papers
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Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
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Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
ASTRA reframes transition-state search as guided diffusion inference that samples the isodensity surface between metastable basins and converges to first-order saddles via score differences and physical forces.
MF-PID turns independent diffusion samples into mean-field interacting agents, proving that quadratic interactions yield exact linear mean interpolation and delivering 19-24% energy savings in demand-response control.
Föllmer processes are variationally optimal among generative diffusions because they minimize the impact of drift estimation error on path-space KL divergence, rendering different interpolation schedules statistically equivalent.
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QMC applied to Euler-Maruyama yields faster sampling-error decay than Monte Carlo, and the new MSTG method based on exact simulation achieves super-exponential truncation-error decay that sharply reduces integration dimension.
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citing papers explorer
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OP-GRPO: Efficient Off-Policy GRPO for Flow-Matching Models
OP-GRPO is the first off-policy GRPO method for flow-matching models that reuses trajectories via replay buffer and importance sampling corrections, matching on-policy performance with 34.2% of the training steps.
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Flow-GRPO: Training Flow Matching Models via Online RL
Flow-GRPO is the first online RL method for flow matching models, raising GenEval accuracy from 63% to 95% and text-rendering accuracy from 59% to 92% with little reward hacking.
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Chameleon: Style-Content Disentangled Framework for Cross-Domain Object Compositing
Chameleon proposes the first large-scale cross-domain compositing dataset and a disentangled encoder plus gated diffusion transformer that outperforms prior in-domain and cross-domain methods on plausibility and fidelity.
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YoCausal: How Far is Video Generation from World Model? A Causality Perspective
YoCausal benchmark shows video diffusion models detect the arrow of time but lack genuine causal understanding relative to humans.
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Let EEG Models Learn EEG
JET is a conditional flow matching framework that generates EEG as continuous raw sequences with added constraints for spectral and temporal properties, achieving over 40% lower TS-FID than prior discrete denoising methods on three benchmarks.
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Linear-DPO: Linear Direct Preference Optimization for Diffusion and Flow-Matching Generative Models
Linear-DPO replaces sigmoid utility with linear utility and adds EMA reference to improve preference alignment in diffusion and flow-matching text-to-image models.
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Functionalization via Structure Completion and Motion Rectification
Object functionalization is cast as neural graph completion over a functional graph of parts, contacts, and motions, followed by geometry realization that also rectifies erroneous motions, demonstrated on furniture with a new paired dataset.
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Towards Generalized Image Manipulation Localization via Score-based Model
DiffIML applies score-based generative modeling to image manipulation localization, recovering coherent masks iteratively from noise to improve generalization on unseen manipulation types.
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HIR-ALIGN: Enhancing Hyperspectral Image Restoration via Diffusion-Based Data Generation
HIR-ALIGN augments limited target data for hyperspectral restoration by creating proxy clean images, synthesizing aligned HSIs with blur-robust diffusion and warp-based transfer, then finetuning models to lower target-domain risk.
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Edit-Compass & EditReward-Compass: A Unified Benchmark for Image Editing and Reward Modeling
Edit-Compass and EditReward-Compass are new unified benchmarks for fine-grained image editing evaluation and realistic reward modeling in reinforcement learning optimization.
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Amortized Guidance for Image Inpainting with Pretrained Diffusion Models
AID amortizes guidance for diffusion inpainting by training a reusable module via an auxiliary Gaussian formulation and continuous-time actor-critic algorithm, improving quality-speed trade-off with under 1% overhead.
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Adaptive Subspace Projection for Generative Personalization
A training-free adaptive subspace projection method mitigates semantic collapsing in generative personalization by isolating and adjusting drift in a low-dimensional subspace using the stable pre-trained embedding as anchor.
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Arena as Offline Reward: Efficient Fine-Grained Preference Optimization for Diffusion Models
ArenaPO infers Gaussian capability distributions from pairwise preferences and applies truncated-normal latent inference to derive fine-grained offline rewards for preference optimization of text-to-image diffusion models.
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DBMSolver: A Training-free Diffusion Bridge Sampler for High-Quality Image-to-Image Translation
DBMSolver is a new training-free sampler using exponential integrators that reduces NFEs by up to 5x and improves quality in diffusion bridge model-based image-to-image translation tasks.
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Oracle Noise: Faster Semantic Spherical Alignment for Interpretable Latent Optimization
Oracle Noise optimizes diffusion model noise on a Riemannian hypersphere guided by key prompt words to preserve the Gaussian prior, eliminate norm inflation, and achieve faster semantic alignment than Euclidean methods.
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$Z^2$-Sampling: Zero-Cost Zigzag Trajectories for Semantic Alignment in Diffusion Models
Z²-Sampling implicitly realizes zero-cost zigzag trajectories for curvature-aware semantic alignment in diffusion models by reducing multi-step paths via operator dualities and temporal caching while synthesizing a directional derivative penalty.
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Dream-Cubed: Controllable Generative Modeling in Minecraft by Training on Billions of Cubes
Dream-Cubed releases a billion-scale voxel dataset and 3D diffusion models that generate controllable Minecraft worlds by operating directly on blocks.
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HP-Edit: A Human-Preference Post-Training Framework for Image Editing
HP-Edit introduces a post-training framework and RealPref-50K dataset that uses a VLM-based HP-Scorer to align diffusion image editing models with human preferences, improving outputs on Qwen-Image-Edit-2509.
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Learning to Credit the Right Steps: Objective-aware Process Optimization for Visual Generation
OTCA improves GRPO training for visual generation by estimating step importance in trajectories and adaptively weighting multiple reward objectives.
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Generative Texture Filtering
A two-stage fine-tuning strategy on pre-trained generative models enables effective texture filtering that outperforms prior methods on challenging cases.
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Long-Text-to-Image Generation via Compositional Prompt Decomposition
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Structure-Adaptive Sparse Diffusion in Voxel Space for 3D Medical Image Enhancement
A sparse voxel-space diffusion method with structure-adaptive modulation achieves up to 10x training speedup and state-of-the-art results for 3D medical image denoising and super-resolution.
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Beyond Reconstruction: Reconstruction-to-Vector Diffusion for Hyperspectral Anomaly Detection
R2VD redefines reconstruction as the origin for residual-guided vector diffusion across PPE, GMP, RSM, and VDI stages to achieve superior anomaly detectability and background suppression on eight datasets.
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Novel View Synthesis as Video Completion
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HumANDiff: Articulated Noise Diffusion for Motion-Consistent Human Video Generation
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1.x-Distill: Breaking the Diversity, Quality, and Efficiency Barrier in Distribution Matching Distillation
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VOSR: A Vision-Only Generative Model for Image Super-Resolution
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Drift-AR: Single-Step Visual Autoregressive Generation via Anti-Symmetric Drifting
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SHARP: Spectrum-aware Highly-dynamic Adaptation for Resolution Promotion in Remote Sensing Synthesis
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FrameDiT: Diffusion Transformer with Matrix Attention for Efficient Video Generation
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Improving Text-to-Image Generation with Intrinsic Self-Confidence Rewards
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MultiAnimate: Pose-Guided Image Animation Made Extensible
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Exploring Cross-Modal Flows for Few-Shot Learning
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Single-Step Reconstruction-Free Anomaly Detection and Segmentation via Diffusion Models
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UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Models
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Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference
Latent Consistency Models enable high-fidelity text-to-image generation in 2-4 steps by directly predicting solutions to the probability flow ODE in latent space, distilled from pre-trained LDMs.
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Human Motion Diffusion Model
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High-Resolution Image Synthesis with Latent Diffusion Models
Latent diffusion models achieve state-of-the-art inpainting and competitive results on unconditional generation, scene synthesis, and super-resolution by performing the diffusion process in the latent space of pretrained autoencoders with cross-attention conditioning, while cutting computational and
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ExpoCM: Exposure-Aware One-Step Generative Single-Image HDR Reconstruction
ExpoCM enables fast one-step single-image HDR reconstruction via exposure-dependent perturbations and region-conditioned consistency trajectories derived from a probability flow ODE.
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Few-step Generative Models as Lossy Compression
Few-step generative models can be reformulated as lossy codecs in the reverse channel coding framework without retraining, yielding faster encoding/decoding on low-resolution image benchmarks.
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Colored Noise Diffusion Sampling
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minWM: A Full-Stack Open-Source Framework for Real-Time Interactive Video World Models
minWM supplies an end-to-end pipeline that fine-tunes bidirectional T2V/TI2V models with camera control then distills them via Causal Forcing into few-step autoregressive generators for low-latency rollout.
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RiT: Vanilla Diffusion Transformers Suffice in Representation Space
A vanilla Diffusion Transformer trained via x-prediction on frozen DINOv2 features reaches FID 1.14 on ImageNet 256x256 with fewer parameters and faster sampling than prior DiT variants.
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Pareto-Enhanced Portrait Generation: Vision-Aligned Text Supervision for Alignment, Realism, and Aesthetics
A feature supervision approach using SigLIP 2 extracts multi-granularity vision-aligned text representations to supervise MM-DiT image branches, pushing the Pareto frontier for portrait generation across alignment, realism, and aesthetics.
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GeoFlow: Enforcing Implicit Geometric Consistency in Video Generation
GeoFlow adds a geometry-consistency reward based on rigid camera flow and object appearance preservation, integrated via reinforcement fine-tuning to improve geometric coherence in video generation.
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Beyond Point-Wise Matching: Structural Representation Alignment for Accelerating Diffusion Transformers
sREPA enforces structural consistency in relational geometry of pre-trained vision features to accelerate DiT training and improve generation quality.
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GeoQuery: Geometry-Query Diffusion for Sparse-View Reconstruction
GeoQuery replaces corrupted rendering features with geometry-aligned proxy queries and restricts cross-view attention to local windows, enabling robust diffusion-based refinement under extreme view sparsity.
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From Synthetic to Real: Toward Identity-Consistent Makeup Transfer with Synthetic and Real Data
The work creates identity-consistent synthetic makeup data via ConsistentBeauty and adapts models to real images using reinforcement learning in RealBeauty, achieving better identity preservation and real-world performance than prior methods.
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Towards Photorealistic and Efficient Bokeh Rendering via Diffusion Framework
MagicBokeh uses a single diffusion model with alternative training, focus-aware masked attention, and degradation-aware depth estimation to produce photorealistic bokeh on low-res zoomed images.
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InkDiffuser: High-Fidelity One-shot Chinese Calligraphy via Differentiable Morphological Optimization
InkDiffuser generates high-fidelity one-shot Chinese calligraphy using high-frequency enhancement and a differentiable ink structure loss for realistic stroke and ink rendering.