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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The García-Pintos feedback Hamiltonian equals the score function of the quantum trajectory distribution, linking quantum feedback to diffusion-model reversal.
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.
STREAM decouples text and music conditioning in a diffusion transformer via AdaLN for structure and BEAM for beats, plus new Motorica++ dataset and editability metrics, claiming SOTA music alignment with preserved semantics.
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citing papers explorer
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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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Large Language Diffusion Models
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
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Sampling from Flow Language Models via Marginal-Conditioned Bridges
Marginal-conditioned bridges enable training-free sampling from Flow Language Models by drawing clean one-hot endpoints from factorized posteriors and using Ornstein-Uhlenbeck bridges, preserving token marginals and reducing denoising error versus conditional-mean bridges.
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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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Aligning Flow Map Policies with Optimal Q-Guidance
Flow map policies enable fast one-step inference for flow-based RL policies, and FMQ provides an optimal closed-form Q-guided target for offline-to-online adaptation under trust-region constraints, achieving SOTA performance.
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Muninn: Your Trajectory Diffusion Model But Faster
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Discrete Langevin-Inspired Posterior Sampling
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Remix the Timbre: Diffusion-Based Style Transfer Across Polyphonic Stems
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ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space
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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
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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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Guiding Distribution Matching Distillation with Gradient-Based Reinforcement Learning
GDMD replaces raw-sample rewards with distillation-gradient rewards in RL-guided diffusion distillation, yielding 4-step models that surpass their multi-step teachers on GenEval and human preference metrics.
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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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VOSR: A Vision-Only Generative Model for Image Super-Resolution
VOSR shows that competitive generative image super-resolution with faithful structures can be achieved by training a diffusion-style model from scratch on visual data alone, using a vision encoder for guidance and a restoration-oriented sampling strategy.
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MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE
MixGRPO speeds up GRPO for flow-based image generators by restricting SDE sampling and optimization to a sliding window while using ODE elsewhere, cutting training time by up to 71% with better alignment performance.
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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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GeoQuery: Geometry-Query Diffusion for Sparse-View Reconstruction
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Encoding and Decoding Temporal Signals with Spiking Bandpass Wavelets
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DiffATS: Diffusion in Aligned Tensor Space
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How to Train Your Latent Diffusion Language Model Jointly With the Latent Space
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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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Continuous Latent Diffusion Language Model
Cola DLM proposes a hierarchical latent diffusion model that learns a text-to-latent mapping, fits a global semantic prior in continuous space with a block-causal DiT, and performs conditional decoding, establishing latent prior modeling as an alternative to token-level autoregressive language model
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Active Learning for Communication Structure Optimization in LLM-Based Multi-Agent Systems
An ensemble-based information-theoretic active learning method using ensemble Kalman inversion selects valuable tasks to optimize communication structures in LLM multi-agent systems more reliably than random sampling under limited training budgets.
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NoiseRater: Meta-Learned Noise Valuation for Diffusion Model Training
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Delta Score Matters! Spatial Adaptive Multi Guidance in Diffusion Models
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V-GRPO: Online Reinforcement Learning for Denoising Generative Models Is Easier than You Think
V-GRPO makes ELBO surrogates stable and efficient for online RL alignment of denoising models, delivering SOTA text-to-image performance with 2-3x speedups over MixGRPO and DiffusionNFT.
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Fisher Decorator: Refining Flow Policy via a Local Transport Map
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Rein3D: Reinforced 3D Indoor Scene Generation with Panoramic Video Diffusion Models
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Long-Horizon Streaming Video Generation via Hybrid Attention with Decoupled Distillation
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ELT: Elastic Looped Transformers for Visual Generation
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VASR: Variance-Aware Systematic Resampling for Reward-Guided Diffusion
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Towards Robust Content Watermarking Against Removal and Forgery Attacks
ISTS watermarking dynamically controls injection based on prompt semantics and uses two-sided detection to resist removal and forgery attacks in diffusion models.
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Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
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ML-based approach to classification and generation of structured light propagation in turbulent media
ML models classify and generate structured light in turbulence using CNNs and diffusion models enhanced by Bregman distance minimization.
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NavCrafter: Exploring 3D Scenes from a Single Image
NavCrafter generates controllable novel-view videos from one image via video diffusion, geometry-aware expansion, and enhanced 3D Gaussian Splatting to achieve state-of-the-art synthesis under large viewpoint changes.
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MPDiT: Multi-Patch Global-to-Local Transformer Architecture For Efficient Flow Matching and Diffusion Model
MPDiT uses a hierarchical multi-patch design in transformers to lower computation in diffusion models by handling coarse global features first then fine local details, plus faster-converging embeddings.
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LLaDA-V: Large Language Diffusion Models with Visual Instruction Tuning
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MAGI-1: Autoregressive Video Generation at Scale
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Unified Video Action Model
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Regional climate risk assessment from climate models using probabilistic machine learning
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IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models
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IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies
IDQL generalizes IQL into an actor-critic framework and uses diffusion policies for robust policy extraction, outperforming prior offline RL methods.
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Density Evolution: A Multiscale View of Density Estimation
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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CaloArt: Large-Patch x-Prediction Diffusion Transformers for High-Granularity Calorimeter Shower Generation
CaloArt achieves top FPD, high-level, and classifier metrics on CaloChallenge datasets 2 and 3 while keeping single-GPU generation at 9-11 ms per shower by combining large-patch tokenization, x-prediction, and conditional flow matching.
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RealDiffusion: Physics-informed Attention for Multi-character Storybook Generation
RealDiffusion uses heat diffusion as a dissipative prior and a region-aware stochastic process inside a training-free physics-informed attention mechanism to improve multi-character coherence while preserving narrative dynamism in sequential image generation.
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Learning Unified Representations of Normalcy for Time Series Anomaly Detection
U²AD learns unified normal data representations via score-based generative modeling and a novel time-dependent score network to outperform prior methods in accuracy and early anomaly detection for multivariate time series.