Score Matching

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3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Latest papers 20

Sep 30, 2026stat.ML

Discrete Score Matching Enables Causal Discovery from Count Data

Count data pose a challenge for score-matching-based causal discovery: derivatives are unavailable, and simply replacing them with finite differences does not generally suffice for causal discovery. We generalize SCORE's constant-curvature criterion (Rolland et al., 2022) by conditioning on the node's value, yielding the conditional curvature score (CCS) for ordering. We also extend curvature-based parent recovery through the off-diagonal curvature score (OCS), enabling directed acyclic graph (DAG) recovery with both scores constructed from score functions for continuous data and concrete scores for counts. In the bivariate setting, zero CCS exactly characterizes a semiparametric generalized linear model (GLM) conditional form in which the conditional family need not be specified in advance, unlike in classical GLMs. For bivariate semiparametric GLM DAGs under our regularity condition, canonical-parameter nonlinearity is necessary and sufficient for identifiability. In multivariate DAGs, this nonlinearity enables DAG recovery through CCS and OCS. Our framework identifies a new class of semiparametric GLM DAGs that strictly contains the nonlinear Gaussian ANM class identified by SCORE. We introduce DISCO (DIscrete SCOre), a count-DAG recovery algorithm that estimates CCS and OCS using discrete diffusion. Experiments demonstrate accurate DAG recovery across Poisson, negative binomial, binomial, and mixed-family settings, as well as scalability to 1,000-node DAGs on a single GPU.

Euijong Song, Hyewon Park, Gunwoong Park

Department of Statistics Seoul National University, Korea · Interdisciplinary Program in Artificial Intelligence; Institute for Data Innovation in Science, Seoul National University, Korea

Score Matching Causal Discovery Causal Identifiability Generalized Linear Models

Sep 27, 2026cs.LG

Safe Score Matching: Diffusion Policies with Hamilton-Jacobi Reachability for Online Safe Reinforcement Learning

Online safe reinforcement learning (RL) seeks policies that maximize reward while satisfying safety constraints. A popular line of research in safe RL relaxes safety to a soft expected-cost constraint and solves the resulting Constrained Markov Decision Process via primal-dual Lagrangian updates that only enforce safety on average. To address this limitation, hard, state-wise constraints are introduced and often imposed through Hamilton-Jacobi (HJ) reachability. Yet such constraints require solving different objectives in the feasible and infeasible regions: reward maximization in the former, recovery toward the feasible regions in the latter. The resulting target action distributions are inherently multimodal, and this structure poses a fundamental challenge for the Gaussian or deterministic actors used in existing HJ-based safe RL, which often collapse onto suboptimal modes. Diffusion policies provide the expressiveness needed to represent such distributions, and recent work on Q-score matching offers a route to training them for online RL by score regression -- but has been applied only to reward maximization. We propose Safe Score Matching (SSM), an off-policy actor-critic method that adapts Q-score matching to hard-constrained safe RL by gating a two-branch score target with HJ reachability: inside the feasible set, the denoising process degenerates to Q-score matching on actions classified as viable by the HJ critic; outside, a recovery branch biases denoising toward regions with lower worst-case violation. On quadrotor and fixed-wing trajectory-tracking and stabilize-and-avoid benchmarks, SSM attains the best or near-best task performance with low false-safe rates, whereas the primal-dual baseline admits more unsafe behavior and reachability-based baselines tend to be more conservative; on Safety-Gymnasium velocity tasks, SSM attains the lowest cost with competitive reward.

Boyang Li, Matthew Kim, Sylvia Lee Herbert

University of California San Diego

Score Matching Constrained RL Diffusion Policy Safe RL

Sep 10, 2026cs.LG

Generalised Score Matching on Convex Domains

Score matching avoids computing the normalising constant that maximum-likelihood estimation requires. On constrained domains, its generalised variants weight the Fisher divergence so that boundary terms vanish. We derive generalised score matching on open convex subsets of

\mathbb{R}^{d}

as the small-neighbourhood limit of minimum probability flow, in which the geometry of the neighbourhoods determines the weight. Every

C^{2}

positive definite weight arises in this way, including those of classical score matching on

\mathbb{R}^{d}

and of its variants for non-negative data on

\mathbb{R}_{+}^{d}

. For exponential families, we extend the standard convexity, consistency and asymptotic normality results to every such weight and show that the estimator converges to the true parameter under certain boundary conditions. For a truncated Gaussian on a polytope and a Dirichlet distribution on the simplex, proposed estimators attain the lowest median error of all methods compared, in at least 42 of 50 ground-truth configurations.

Nishanth Shetty, Saisuchith Mahajan, Chandra Sekhar Seelamantula

Department of Electrical Engineering Indian Institute of Science, Bengaluru 560012

Score Matching Parameter Estimation

Aug 5, 2026cs.SD

A Dual Evaluation for Music Transcription

Automatic music transcription systems produce sheet music that can be read and played back. We argue that these two targets call for complementary evaluations of notation similarity to a reference score and playback similarity to the original performance, respectively. Our study considers notation similarity metrics from the optical music recognition literature and a wide range of playback-similarity methods validated through a listening study across over 100 participants and 230 piano recordings covering 23 works, 30 performers, and six composers. We find, fortuitously, that the playback similarity metric that correlates best with human judgments, CLEWS, is also the cheapest to run. We also find that the two evaluation dimensions favor different systems among a collection of 24 pipelines formed by pairing eight audio-to-MIDI models with three MIDI-to-score converters, with the latter component systematically determining the favored objective. The complementarity between metrics also holds when adding to the pool Rubato, a new end-to-end system that offers substantially improved notation similarity while remaining competitive, though not the best, on playback similarity.

Ping Wang, Guang Yang, Nazif Can Tamer +2

Score Matching Automatic Music Transcription Music Information Retrieval

Aug 4, 2026stat.ML

Should the Boundary Term Be Learned in Reflected Diffusion? Conormal Trace and Reflection Masking

We study score learning for reflected diffusion on bounded domains. Reflection keeps trajectories feasible but does not ensure that the learned score satisfies the boundary behavior implied by the forward process. With implicit score matching, integration by parts leaves a boundary term, and we show that it depends on one scalar at each boundary point: the diffusion- weighted normal component of the score, or conormal trace. The no-flux condition fixes this value while leaving the re- maining boundary components unrestricted; under anisotropic diffusion it generally differs from the ordinary normal score component. On hyperrectangles, our parametrization enforces the required trace without additional trainable parameters or a stochastic boundary estimator and, under regularity assump- tions, can represent the true score, whereas fixing an incorrect value creates an error that more data cannot remove. We ex- tend the construction to simplices and polygonal domains and identify reflection masking: hard reflection can keep samples feasible even when the learned trace is wrong, so post-reflection metrics may hide the error. Experiments show the clearest separation with less frequent reflection, anisotropic diffusion, and mass near intersections of constraints; under full reflection, final sample placement improves inconsistently, illustrating how hard repair can mask boundary-score errors and decouple score accuracy from downstream generation quality.

Ziyue Wang, Takafumi Kanamori

Institute of Science Tokyo

Score Matching Diffusion Models

Aug 3, 2026stat.ML

A Hyperfinite Framework for Score-Based Generative Modeling

Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus. In this paper, we develop a hyperfinite formulation of score-based generative modeling within the framework of Nonstandard Analysis. Starting from an internal diffusion process on a hyperfinite grid, we derive the associated infinitesimal generator and establish its correspondence with the classical Fokker--Planck equation. We then obtain a hyperfinite backward-mean identity that yields the reverse-time drift and provides a constructive derivation of the reverse-time SDE. Building on these results, we show that minimization of an internal score-matching objective recovers the score function required by the reverse-time dynamics, thereby connecting score estimation with generative sampling directly at the hyperfinite level. Under suitable assumptions, we further derive a hyperfinite Girsanov formula and establish a relationship between likelihood optimization and Fisher-divergence objectives. Finally, we analyze the second-order consistency of the hyperfinite dynamics and show that the leading correction term depends explicitly on the fourth moment of the increment distribution, with the Gaussian value

κ=3

eliminating the leading dispersion contribution. Taken together, these results provide a unified hyperfinite framework for diffusion-based generative modeling--while laying foundations for further extensions--that links discrete grid dynamics, reverse-time diffusion, score matching, and likelihood-based formulations within a common nonstandard setting.

Sunder Ram Krishnan

Kerala School of Mathematics, Kozhikode 673571, Kerala, India.

Score Matching Stochastic Differential Equations Score-Based Generative Modeling

Jul 9, 2026stat.ML

Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling

Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory. We show that small forward-marginal error does not guarantee numerical stability. We construct a single smooth score field with arbitrarily small forward-marginal

L^2

error. The learned reverse-time process is nonexplosive, has moments of every order, and can be arbitrarily close to the exact reverse-time process in path-space total variation. Yet its Euler--Maruyama discretizations converge in probability while every positive moment diverges. Thus weak convergence can hold even though every Wasserstein distance

W_p

,

p\ge1

, diverges. The same failure can occur within one fixed finite neural architecture. We construct a family of bounded, globally Lipschitz denoisers for which both the forward-marginal error and the path-space total variation distance tend to zero, while their Euler--Maruyama endpoints diverge in every

W_p

. For compactly supported data, we also give a simple positive result. Projecting the learned denoiser onto a known bounded closed convex set containing the support preserves pointwise accuracy, gives grid-uniform moment bounds, and yields Wasserstein convergence under mild local regularity. Experiments with a small fixed DiT-style network show large growth along rare numerical trajectories and its suppression by denoiser projection, while overall trajectory errors remain small.

Yiwei Zhou

Score Matching Diffusion Sampling

Jul 5, 2026stat.ML

Tightening the Score Matching Gap for Diffusion Models

Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution. Their training and evaluation primarily rely on an Evidence Lower Bound (ELBO), which relates the Kullback-Leibler (KL) divergence of model samples to the score matching loss along the path, which serves as a tractable surrogate. The difference between sample quality and the score matching loss produced by this bound leads to the \emph{score matching gap}, which is known to be tight in the worst-case but not descriptive of sample quality in general. In this work, we provide a theoretical analysis of this gap, developing tighter bounds for three metrics: KL divergence, reverse KL divergence, and Wasserstein distance, effectively exploiting the regularity of the class of score estimators. Our results suggest that the quality of the score approximation has more impact on closing the score matching gap for low noise scales. To obtain these bounds, our key technical insight is to exploit the contraction properties of the backward processes. In particular, we rely on entropy flows, logarithmic Sobolev inequalities and reflection couplings, rigorously linking the ergodicity of the Langevin diffusion to the score matching gap problem.

Benjamin Dupuis, Tyler Farghly, Maxime Haddouche +2

INRIA - CNRS - D´epartement d’Informatique de l’Ecole Normale Sup´erieure - PSL Research University, France · Ecole Polytechnique - CMAP, IP Paris, Palaiseau, France

Score Matching Score-Based Generative Modeling Diffusion Models

Jun 18, 2026cs.LG

Global Convergence of Gradient Descent for Score Matching in Gaussian Mixtures via Reverse Fisher Divergence

The score matching problem is a central training objective in modern generative modeling, diffusion models, fitting unnormalized statistical models, and inverse problems. A standard approach is to minimize the forward Fisher divergence, where the expectation is taken with respect to the teacher distribution. However, recent results show that even in simple Gaussian mixture model settings, this objective can lead to undesirable and initialization-dependent convergence behavior. In this paper, we study an alternative objective: the reverse Fisher divergence, where the expectation is taken with respect to the student distribution. We analyze gradient descent (GD) for fitting Gaussian mixture models and show that this change in the objective leads to significantly better optimization properties. First, when the teacher distribution is a single Gaussian and the student is a Gaussian mixture model with fixed weights and identity covariances, we prove the global convergence of GD from arbitrary initializations. Second, we extend the analysis to the case where the teacher is also a Gaussian mixture model and prove global convergence guarantees under a global random initialization scheme and a

\widetildeΩ(1)

-separation assumption on the target means. In particular, with high probability, each student component converges near its closest teacher component, and we provide conditions under which the student distribution converges in total variation distance. Our proofs rely on a new Lyapunov-based analysis of the gradient descent dynamics, showing that the reverse Fisher divergence has a much more favorable optimization landscape than the forward Fisher divergence.

Alexander Tyurin

AXXX, Moscow, Russia · Applied AI Institute, Moscow, Russia

Score Matching Optimization Convergence Analysis Gaussian Mixture Models Gradient Descent Dynamics

Jun 4, 2026stat.ML

Diffusion Models Observe Only Gradients: A Geometric Perspective on Score Matching Errors

Score-based diffusion models are typically trained by minimizing the

L^2

score matching error, and standard theoretical analyses rely on this quantity to bound the sampling discrepancy between the learned and target distributions. We show the

L^2

score error is not the right intrinsic measure of marginal distributional quality: a learned diffusion model can incur arbitrarily large

L^2

score error while perfectly matching the target distribution. By decomposing score errors into a gradient and a solenoidal component (a Helmholtz-Hodge decomposition), we identify the geometric reason behind this: only the gradient component enters the marginal Fokker-Planck dynamics, while the solenoidal component is structurally invisible. We make this precise in three results. First, building on the corrected geometry, we prove an impossibility result: no monotone function of the

L^2

score error can uniformly lower bound any divergence between the learned and target distributions. Second, we derive an upper bound on the Kullback-Leibler divergence that depends only on the observable gradient component of the error, tightening the standard Girsanov bound for generic score networks, and identifying its looseness as the cost of operating on path-space rather than marginal-space dynamics. Third, we give a tractable estimator of the gradient component via a dual Sobolev identity, which is shown to empirically correlate substantially better with sample quality than the full

L^2

error.

Naïl B. Khelifa, Richard E. Turner, Ramji Venkataramanan

University of Cambridge

Score Matching Hodge Decomposition Score-Based Generative Modeling Diffusion Models

May 30, 2026cs.LG

Torus Graphs for Large Scale Neural Phase Analysis

Oscillatory neural signals such as electroencephalography (EEG) and local field potentials (LFPs) show phase relationships that coordinate communication across brain regions. Modern recordings capture hundreds of channels across many frequency bins, yet standard phase analyses are restricted to only a few variables. The Torus Graph (TG) model, an exponential-family distribution over phases whose univariate and pairwise potentials generalize von Mises distributions, infers principled structure among oscillations but models only static, undirected dependencies and is limited to

\sim \! 100

variables because its score matching inference scales as

\mathcal{O}(d^{6})

. We introduce a stochastic score matching procedure that reduces the per-iteration cost to

\mathcal{O}(d^{2})

, enabling inference on datasets with thousands of variables. This scalable foundation supports analyses of 1,860 frequency-phase features from multi-electrode LFPs and enables two extensions previously inaccessible to TGs or classical circular statistics: (i) a TG Hidden Markov Model capturing state-dependent phase-coupling changes (e.g., spindle-related states during sleep) and (ii) an autoregressive TG inferring directional interactions via transfer-entropy estimation. Applied to LFP recordings, these models reveal state-dependent phase-interaction patterns between wakefulness and NREM sleep. Together, they enable systematic, large-scale mapping of dynamic and directional phase relationships across brain and cognitive states.

Jack Goffinet, Casey Hanks, David E. Carlson

Department of Computer Science, Duke University, Durham NC, USA · Departments of Civil and Environmental Engineering; Biostatistics and Bioinformatics; and Electrical and Computer Engineering, Duke University, Durham NC, USA

Score Matching Sequence Modeling Hidden Markov Models

May 29, 2026cs.CV

Score-Control for Hallucination Reduction in Diffusion Models

Diffusion models have emerged as the backbone of modern generative AI, powering advances in vision, language, audio and other modalities. Despite their success, they suffer from hallucinations, implausible samples that lie outside the support of true data distribution, which degrade reliability and trust. In this work, we first empirically confirm previously proposed hypothesis that score smoothness causes hallucinations in Image Generation diffusion models and provide a density-based perspective. We further formalize this notion by linking the hallucinations probability mass to lipschitz constant of the learned score function. Motivated by this, we introduce a Variance-Guided Score Modulation (VSM) strategy that controls the score Jacobian, in turn reducing score smoothness and better approximating the ground truth score that decreases hallucinations. Empirical results on synthetic and real-world datasets demonstrate that our approach reduces hallucinations (up to ~25%) while maintaining high fidelity and diversity, providing a principled step toward more reliable diffusion-based image generation. We also propose two benchmark datasets with extreme semantic variation for systematic hallucination evaluation. Code and Datasets are publicly available at https://github.com/bhosalems/VSM.

Mahesh Bhosale, Naresh Kumar Devulapally, Abdul Wasi +3

University at Buffalo Buffalo, NY, USA

Score Matching Diffusion-Based Image Generation Image Generation Evaluation Diffusion Models

May 25, 2026stat.ML

Rao-Blackwellized Score Matching on Manifolds

We study denoising score matching (DSM) when the latent distribution is supported on a smooth embedded manifold

M \subset \mathbb{R}^D

. Under ambient Gaussian corruption, the tangent denoising target contains a singular normal-fiber noise channel whose variance diverges as

d/σ^2

as

σ\to 0^+

. We show that conditioning on the nearest-point projection

π(X)

canonically removes this singularity: the resulting conditional expectation is the unique

L^2

-optimal Rao-Blackwellized predictor of the tangent DSM target among all estimators depending only on the projected observation

π(X)

. We then compute the small-noise expansion of this canonical target and show that it equals the intrinsic Riemannian score up to an explicit order-

σ^2

correction that decomposes into an intrinsic Tweedie term and an extrinsic curvature term involving the Weingarten and Ricci operators. In the flat case, the construction reduces exactly to ordinary lower-dimensional Gaussian DSM, while on

S^d

the extrinsic correction simplifies to the scalar factor

(1-d/2)\nabla_M \log q

; this extrinsic

σ^2

correction cancels identically on

S^2

, though the intrinsic Tweedie term remains.

Divit Rawal

Department of Statistics, University of California, Berkeley, Berkeley CA, U.S.A..

Score Matching Score-Based Generative Modeling

May 21, 2026stat.ML

Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation

Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likelihood estimation for multimodal distributions with well-separated modes, which are commonly encountered in practical applications. We compare a novel diffusion-based denoising score matching estimator (DDSME) to the vanilla score matching estimator (SME) in this scenario. In particular, we prove statistical guarantees for both estimators, showing that the error bound for the vanilla SME worsens when the separation between the modes increases, which can be avoided in case of the DDSME with suitable hyperparameter tuning. This provides a novel theoretical explanation for the superior behavior of diffusion-based score matching over the vanilla version.

Benedikt Lütke Schwienhorst, Nadja Klein, Johannes Lederer

Department of Mathematics University of Hamburg Hamburg, Germany · Scientific Computing Center Karlsruhe Institute of Technology2026 Karlsruhe, Germany · Department of MathematicsMay University of Hamburg Hamburg, Germany21

Score Matching Parameter Estimation Score-Based Generative Modeling Diffusion Models

May 13, 2026cs.LG

Finite Sample Bounds for Learning with Score Matching

Learning of continuous exponential family distributions with unbounded support remains an important area of research for both theory and applications in high-dimensional statistics. In recent years, score matching has become a widely used method for learning exponential families with continuous variables due to its computational ease when compared against maximum likelihood estimation. However, theoretical understanding of the statistical properties of score matching is still lacking. In this work, we provide a non-asymptotic sample complexity analysis for learning the structure of exponential families of polynomials with score matching. The derived sample bounds show a polynomial dependence on the model dimension. These bounds are the first of its kind, as all prior work has shown only asymptotic bounds on the sample complexity.

Devin Smedira, Abhijith Jayakumar, Sidhant Misra +2

Operations Research Center, Massachusetts Institute of Technology · Theoretical division, Los Alamos National Lab

Score Matching Sample Complexity Statistical Learning Theory

May 13, 2026math.OC

Proximal-Based Generative Modeling for Bayesian Inverse Problems

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we propose a novel proximal-based generative modeling (PGM) framework that rigorously circumvents explicit likelihood evaluation. Our framework is built upon a theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization in nonsmooth optimization. This enables a new sampling mechanism driven by the proposed Moreau score, which admits a closed-form expression via proximal operators. Moreover, we introduce Moreau score matching to learn the proximal operators that rely solely on samples drawn from the prior distribution. Theoretically, PGM eliminates the early-stopping bias inherent in the score-based diffusion model and achieves non-asymptotic convergence. Experiments demonstrate that PGM significantly surpasses state-of-the-art methods in reconstruction quality and sampling time.

Boyang Zhang, Zhiguo Wang, Ya-Feng Liu

School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences, Beijing, China · Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China · School of Mathematics, Sichuan University, Chengdu, China +2

Score Matching Bayesian Inverse Problems Generative Modeling Diffusion-Based Inverse Problems Score-Based Generative Modeling

May 7, 2026hep-lat

Diffusion model for SU(N) gauge theories

Implicit score matching provides a computationally efficient approach for training diffusion models and generating high-quality samples from complex distributions. In this work, we develop a score-matching framework for SU(N) lattice gauge theories, which can be extended to other Lie groups. We apply the method to SU(3) gauge configurations with the Wilson gauge action in two and four dimensions and assess the quality of the generated samples by comparison with Hybrid Monte Carlo (HMC) simulations. We show that the diffusion models can be successfully trained and applied for sampling the Wilson gauge action. For large values of inverse coupling, accurate reverse-time integration requires predictor-corrector schemes, for which we introduce a corrector based on Hamiltonian molecular dynamics. While the corrector significantly improves sampling quality, it also increases the computational cost. We outline several strategies for improving sampling efficiency.

Javad Komijani, Marina K. Marinkovic, Lara Turgut

Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

Score Matching Diffusion Sampling High-Energy Physics Diffusion Models

Apr 28, 2026quant-ph

Quantum Dynamics via Score Matching on Bohmian Trajectories

We solve the time-dependent Schrödinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under the classical potential supplemented by a quantum potential depending on the score function of the evolving density. These non-crossing Bohmian trajectories form a continuous normalizing flow governed by the score. We parametrize the score with a neural network and minimize a self-consistent Fisher divergence between the network and the score of the resulting density. We prove that the zero-loss minimizer of this self-consistent objective recovers Schrödinger dynamics for nodeless wave functions, a condition naturally met in quantum vibrations of atoms. We demonstrate the approach on wavepacket splitting in a double-well potential and anharmonic vibrations of a Morse chain. By recasting real-time quantum dynamics as a self-consistent score-driven normalizing flow, this framework opens the time-dependent Schrödinger equation to the rapidly advancing toolkit of modern generative modeling.

Lei Wang

Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Score Matching PDE Solving Score-Based Generative Modeling

Dec 23, 2025cs.LG

Control Variate Score Matching for Diffusion Models

Sampling from unnormalized probability densities is a pervasive challenge across the computational and physical sciences. Diffusion models provide a powerful generative framework for this task, but their success relies on accurately estimating the score of the perturbed target distribution. Current approaches face a dichotomy between two standard estimation methods: the Denoising Score Identity (DSI) requires data samples and exhibits high variance at low noise levels, whereas the Target Score Identity (TSI) relies on the energy function and suffers from diverging variance at high noise levels. In this work, we reconcile both approaches by introducing the Control Variate Score Identity (CVSI), an unbiased estimator with an analytically optimal, state- and time-dependent control coefficient that theoretically minimizes variance over the entire diffusion process. CVSI serves as a robust plug-in estimator that significantly enhances performance and efficiency in data-free sampler learning and training-free diffusion sampling. These gains scale to complex, high-dimensional energy-based models.

Khaled Kahouli, Romuald Elie, Klaus-Robert Müller +3

1Google DeepMind · 2BIFOLD – Berlin Institute for the Foundations of Learning and Data · 3Machine Learning Group, Technische Universität Berlin +2

Score Matching Diffusion Model Sampling Score-Based Generative Modeling Variance Reduction

Sep 29, 2025cs.LG

Advantage Weighted Matching: Aligning RL with Pretraining in Diffusion Models

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where both pre-training and RL post-training stages are grounded in the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the score/flow-matching loss and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This simple yet effective design yields substantial benefits: on the GenEval, OCR, and PickScore benchmarks, AWM delivers up to a

34\times

speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching

Shuchen Xue, Chongjian Ge, Shilong Zhang +2

UCAS · Adobe Research · HKU +1

Score Matching Diffusion Model Alignment T2I Generation RL for Image Generation RL for Diffusion Models