Newton Matching for Generative Modeling: A Unified Framework for Fine-Tuning and Sampling

• URL: http://arxiv.org/abs/2609.05727v1
• Date: Fri, 04 Sep 2026 21:17:05 GMT
• Title: Newton Matching for Generative Modeling: A Unified Framework for Fine-Tuning and Sampling
• Abstract summary: We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling.<n>We shift the paradigm from isolated losses to iterative optimization over canonical models.<n>Our work advances the theory and algorithms of reinforcement learning for generative models.
• Score: 4.589496709268605
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling. The target is $π\proptoμe^{τr}$, where $r$ is the reward, $τ>0$ the inverse temperature, and $μ$ denotes the pretrained model's terminal density for fine-tuning or the constant $1$ for sampling. We shift the paradigm from isolated losses to iterative optimization over canonical models: population minimizers of standard conditional matching for terminal densities. Under compatible smooth-realization assumptions, canonical velocities form a manifold diffeomorphic to the density manifold. Transporting the Fisher-Rao metric and mixture connection to this manifold, we show that the reverse-KL Hessian equals the metric, so the Newton direction coincides with the negative Fisher-Rao gradient. At terminal density $ρ$, each stage takes a tangential step generated by the regularized reward $r-\frac1τ\log(ρ/μ)$, followed by terminal-density-preserving canonicalization. This canonical retraction yields an exact finite-stepsize density characterization. For the ideal iteration, we prove strict reverse-KL descent away from the target for $0 < η\le τ$, global convergence under mild conditions, and local quadratic convergence for full steps ($η=τ$). Covariance and gradient forms, each with forward or reverse regression-pair constructions, yield sample-wise tangential-update losses with the same population minimizer, without importance sampling or full-trajectory backpropagation. We develop approximate updates and define critical-point consistency as vanishing tangential displacement if and only if $ρ=π$. We recover representative methods as exact realizations, critical-point-consistent approximations, or objective-altering variants, enabling modular algorithm design. Our work advances the theory and algorithms of reinforcement learning for generative models.

Related papers

• Particle Dynamics of Flow Matching and Classifier-Free Guidance from a Stagewise Geometry Perspective [3.9423546337949253]
  Flow matching, together with guidance (CFG), is widely used in generative modeling.<n>We establish a unified stagewise geometric theory attraction attraction for both dynamics.<n>We further show that a general time schedule $a(t)$ replaces the $O(1-t)$ decay by $O(1-a(t)$.
  arXiv  Detail & Related papers  (2026-09-07T02:33:36Z)
• Provably adaptive sampling with uniform and remasking discrete diffusion models [9.180350432640912]
  We study a first-order sampler based on the leave-one-out denoiser for uniform and remasking processes.<n>Our main result establishes an adaptive sampling guarantee.<n> Numerical experiments on structured synthetic distributions illustrate the predicted dimension-adaptive behavior.
  arXiv  Detail & Related papers  (2026-08-24T17:54:51Z)
• Towards Scalable Persistence-Based Topological Optimization [44.16669776030478]
  Persistence-based topological optimization deforms a point cloud $X subset mathbbRd$ by minimizing objectives of the form $L(X) = ell(mathrmDgm(X))$, where $mathrmDgm(X)$ is a persistence diagram.<n>In practice, optimization is limited by two coupled issues: persistent homology is typically computed on subsamples, and the resulting topological gradients are highly sparse, with only a few anchor points receiving nonzero updates.
  arXiv  Detail & Related papers  (2026-05-09T15:47:20Z)
• Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees [9.180350432640912]
  We study the sampling efficiency of score-based discrete diffusion models under a continuous-time Markov chain (CTMC) formulation.<n>For uniform discrete diffusion, we show that the $$-leaping algorithm achieves an complexity of order $tilde O(d/varepsilon)$.<n>For masking discrete diffusion, we introduce a modified $$-leaping sampler whose convergence rate is governed by an intrinsic information-theoretic quantity.
  arXiv  Detail & Related papers  (2026-02-16T18:48:17Z)
• Stabilizing Fixed-Point Iteration for Markov Chain Poisson Equations [49.702772230127465]
  We study finite-state Markov chains with $n$ states and transition matrix $P$.<n>We show that all non-decaying modes are captured by a real peripheral invariant subspace $mathcalK(P)$, and that the induced operator on the quotient space $mathbbRn/mathcalK(P) is strictly contractive, yielding a unique quotient solution.
  arXiv  Detail & Related papers  (2026-01-31T02:57:01Z)
• Inference-Time Scaling of Diffusion Language Models with Particle Gibbs Sampling [70.8832906871441]
  We study how to steer generation toward desired rewards without retraining the models.<n>Prior methods typically resample or filter within a single denoising trajectory, optimizing rewards step-by-step without trajectory-level refinement.<n>We introduce particle Gibbs sampling for diffusion language models (PG-DLM), a novel inference-time algorithm enabling trajectory-level refinement while preserving generation perplexity.
  arXiv  Detail & Related papers  (2025-07-11T08:00:47Z)
• Variance Reduction for the Independent Metropolis Sampler [11.074080383657453]
  We prove that if $pi$ is close enough under KL divergence to another density $q$, an independent sampler that obtains samples from $pi$ achieves smaller variance than i.i.d. sampling from $pi$. We propose an adaptive independent Metropolis algorithm that adapts the proposal density such that its KL divergence with the target is being reduced.
  arXiv  Detail & Related papers  (2024-06-25T16:38:53Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions.<n>For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling.<n>We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal [70.15267479220691]
  We consider and analyze the sample complexity of model reinforcement learning with a generative variance-free model. Our analysis shows that it is nearly minimax-optimal for finding an $varepsilon$-optimal policy when $varepsilon$ is sufficiently small.
  arXiv  Detail & Related papers  (2022-05-27T19:39:24Z)
• Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction [63.41789556777387]
  Asynchronous Q-learning aims to learn the optimal action-value function (or Q-function) of a Markov decision process (MDP) We show that the number of samples needed to yield an entrywise $varepsilon$-accurate estimate of the Q-function is at most on the order of $frac1mu_min (1-gamma)5varepsilon2+ fract_mixmu_min (1-gamma)$ up to some logarithmic factor.
  arXiv  Detail & Related papers  (2020-06-04T17:51:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.