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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Generative Modeling with Flux Matching
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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Quotient-Space Diffusion Models
Quotient-space diffusion models generate correct symmetric distributions by removing redundancy on the quotient space, simplifying learning and improving results on small molecules and proteins under SE(3) symmetry.
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Query Lower Bounds for Diffusion Sampling
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
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Denoising Diffusion Implicit Models
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
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Generative Modeling by Value-Driven Transport
A control-theoretic linear program yields value-driven transport policies for generative modeling with straight paths and simulation-free training.
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CAdam: Context-Adaptive Moment Estimation for 3D Gaussian Densification in Generative Distillation
CAdam reinterprets densification in generative 3DGS as signal verification via gradient-moment interference, quantile context, and SNR gating to achieve large reductions in primitive count with comparable quality.
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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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Bridging Domain Gaps with Target-Aligned Generation for Offline Reinforcement Learning
TCE bridges domain gaps in offline RL by selectively using source data or generating target-aligned transitions via a dual score-based model, outperforming baselines in experiments.
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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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On the Approximation Complexity of Matrix Product Operator Born Machines
MPO-BMs have NP-hard KL approximation in continuous settings but admit efficient polynomial-bond-dimension approximations with provable KL guarantees for structured targets under locality and spectral-gap conditions.
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Discrete Langevin-Inspired Posterior Sampling
ΔLPS is a gradient-guided discrete posterior sampler for inverse problems that works with masked or uniform discrete diffusion priors and outperforms prior discrete methods on image restoration tasks.
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A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots
Wasserstein Lagrangian Mechanics formalizes second-order dynamics in Wasserstein space and provides an algorithm to learn them from observed marginals without specifying the Lagrangian, outperforming gradient flows on various dynamics.
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Kurtosis-Guided Denoising Score Matching for Tabular Anomaly Detection
K-DSM uses per-feature kurtosis to set noise scales in DSM, enabling effective single-scale anomaly detection on tabular benchmarks in both semi-supervised and unsupervised settings.
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Beyond Penalization: Diffusion-based Out-of-Distribution Detection and Selective Regularization in Offline Reinforcement Learning
DOSER detects OOD actions via diffusion-model denoising error and applies selective regularization based on predicted transitions, proving gamma-contraction with performance bounds and outperforming priors on offline RL benchmarks.
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PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution
PODiff performs conditional diffusion in a fixed, variance-ordered POD latent space to enable efficient probabilistic super-resolution of high-dimensional scientific fields with lower memory and better-calibrated uncertainty than pixel-space or dropout baselines.
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GD4: Graph-based Discrete Denoising Diffusion for MIMO Detection
GD4 is a graph-based discrete denoising diffusion method for MIMO detection that yields higher-quality suboptimal solutions than prior diffusion detectors and classical baselines under similar compute budgets in both under- and over-determined settings.
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ABC: Any-Subset Autoregression via Non-Markovian Diffusion Bridges in Continuous Time and Space
ABC enables any-subset autoregressive generation of continuous stochastic processes via non-Markovian diffusion bridges that track physical time and allow path-dependent conditioning.
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Frequency-Forcing: From Scaling-as-Time to Soft Frequency Guidance
Frequency-Forcing guides pixel flow-matching with a data-derived low-frequency auxiliary stream to softly enforce scale-ordered generation, improving FID on ImageNet-256 over baselines.
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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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NI Sampling: Accelerating Discrete Diffusion Sampling by Token Order Optimization
NI Sampling accelerates discrete diffusion language models up to 14.3 times by training a neural indicator to select which tokens to sample at each step using a trajectory-preserving objective.
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Grokking of Diffusion Models: Case Study on Modular Addition
Diffusion models show grokking on modular addition by composing periodic operand representations in simple data regimes or by separating arithmetic computation from visual denoising across timesteps in varied regimes.
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Reinforcement Learning via Value Gradient Flow
VGF solves behavior-regularized RL by transporting particles from a reference distribution to the value-induced optimal policy via discrete value-guided gradient flow.
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Diffusion Processes on Implicit Manifolds
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
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Sample-efficient evidence estimation of score based priors for model selection
DiME estimates model evidence for diffusion priors by integrating time-marginals from posterior sampling, enabling efficient prior selection and misfit diagnosis in ill-posed inverse problems.
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QuantVLA: Scale-Calibrated Post-Training Quantization for Vision-Language-Action Models
QuantVLA is the first post-training quantization framework for VLA models that quantizes the diffusion transformer action head and reports higher task success rates than full-precision baselines with roughly 70% memory savings on the quantized components.
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Not All Denoising Steps Are Equal: Model Scheduling for Faster Masked Diffusion Language Models
Early and late denoising steps in masked diffusion LMs are robust to smaller-model replacement, enabling 17% FLOPs reduction with modest generative quality loss.
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SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants
SplineFlow uses B-spline interpolation inside flow matching to jointly construct stable conditional paths that satisfy multi-marginal constraints for dynamical systems with irregular observations.
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From Navigation to Refinement: Revealing the Two-Stage Nature of Flow-based Diffusion Models through Oracle Velocity
Flow matching models follow a two-stage process of navigation across data modes then refinement to nearest samples, revealed by exact computation of the oracle marginal velocity field.
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Beyond Binary Out-of-Distribution Detection: Characterizing Distributional Shifts with Multi-Statistic Diffusion Trajectories
DISC extracts multi-statistic trajectories from diffusion denoising to both detect and classify types of distributional shifts in OOD data.
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Score-based Membership Inference on Diffusion Models
Presents SimA, a score-based single-query membership inference attack for diffusion models and LDMs that uses denoiser output norm to reveal training set proximity and outperforms multi-query baselines on eight datasets.
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Diffusion Models Beat GANs on Image Synthesis
Diffusion models with architecture improvements and classifier guidance achieve superior FID scores to GANs on unconditional and conditional ImageNet image synthesis.
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Latent Diffusion Pretraining for Crystal Property Prediction
CrysLDNet combines VAE and latent diffusion pretraining on unlabeled crystals to improve graph encoder performance on property prediction by about 4-5% on JARVIS and MP datasets.
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Variance Reduction for Expectations with Diffusion Teachers
CARV amortizes upstream diffusion teacher costs over noise resamples with timestep importance sampling and stratified-inverse-CDF sampling, delivering 2-3x effective compute gains in text-to-3D experiments and order-of-magnitude variance cuts in single-step distillation.
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Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment
REPA-P aligns intermediate representations in diffusion models with physical states using first-principles PDE residuals to accelerate convergence and boost out-of-distribution robustness on PDE tasks.
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Mechanisms of Misgeneralization in Physical Sequence Modeling
Generative sequence models for physical tasks exhibit physical misgeneralization where local prediction errors propagate through physical measurements to distort aggregate distributions over quantities like distance or energy; a data deviation kernel explains and predicts the shifts and supports a内核
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Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
SiLD is a score-matching framework that learns both manifold projection and intrinsic density from a single objective, with proven sample complexity depending only on intrinsic dimension.
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Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing
Recasts sampling-based nonconvex optimization as smoothed gradient descent to obtain non-asymptotic convergence guarantees and introduces the DIDA annealed algorithm that converges to the global optimum.
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DiffATS: Diffusion in Aligned Tensor Space
DiffATS trains diffusion models directly on aligned Tucker tensor primitives that are proven to be homeomorphisms, delivering efficient unconditional and conditional generation across images, videos, and PDE data with high compression.
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FlashMol: High-Quality Molecule Generation in as Few as Four Steps
FlashMol produces chemically valid 3D molecules in 4 steps via distribution matching distillation with respaced timesteps and Jensen-Shannon regularization, matching or exceeding 1000-step teacher performance on QM9 and GEOM-DRUG.
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Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems
Distilled one-step consistency model from optimal-transport flow-matching teacher reconstructs high-fidelity dynamical system flows from low-fidelity data with 12x speedup, half the parameters, and 23.1% better SSIM than scratch-trained baselines.
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Scaling Pretrained Representations Enables Label-Free Out-of-Distribution Detection Without Fine-Tuning
Scaling pretrained representations improves label-free OOD detection on frozen backbones, causing performance gaps between global and local detectors to vanish across vision and language tasks.
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Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees
Error in approximating the tangent conditional score by the unconditional score in diffusion models is bounded by dimension-free conditional mutual information, with a projected-Langevin method outperforming baselines in inpainting and super-resolution.
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A Few-Step Generative Model on Cumulative Flow Maps
Cumulative flow maps unify few-step generative modeling for diffusion and flow models via cumulative transport and parameterization with minimal changes to time embeddings and objectives.
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PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics
PerFlow decouples observation conditioning from physics enforcement in rectified flows using constraint-preserving projections and invariance guarantees for fast, physics-consistent reconstruction of spatiotemporal dynamics.
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NoiseRater: Meta-Learned Noise Valuation for Diffusion Model Training
NoiseRater meta-learns instance-level importance scores for noise in diffusion training via bilevel optimization, then uses a two-stage pipeline to improve efficiency and generation quality on FFHQ and ImageNet.
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Proteo-R1: Reasoning Foundation Models for De Novo Protein Design
Proteo-R1 decouples an MLLM-based understanding expert that selects functional residues from a diffusion-based generation expert that builds protein structures under those explicit constraints.
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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
Fisher Decorator refines flow policies in offline RL via a local transport map and Fisher-matrix quadratic approximation of the KL constraint, yielding controllable error near the optimum and SOTA benchmark results.
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Data Warmup: Complexity-Aware Curricula for Efficient Diffusion Training
Data Warmup accelerates diffusion training on ImageNet by scheduling images from low to high complexity via a foreground-based metric and temperature-controlled sampler, improving FID and IS scores faster than uniform sampling.
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Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
FOT-CFM generates turbulent fields in function space with superior high-order statistics and energy spectra on Navier-Stokes, Kolmogorov flow, and Hasegawa-Wakatani equations compared to baselines.