arXiv subjects

Stanislas Strasman

Publications and source records attributed to Stanislas Strasman.

5 recordsLinked to original sources

arXiv2026

Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Models

Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications. While the statistical properties of their sampling procedures are increasingly well understood, the optimization dynamics underlying their training remain less explored. SGMs are typically trained by minimizing a weighted denoising scorematching objective, yet optimization guarantees with stochastic gradients remain limited. In this work, we study Stochastic Gradient Descent (SGD) for SGMs, contributing results in two complementary regimes. First, for general score parameterizations, we establish a non-convex convergence rate for SGD on the weighted denoising score-matching objective, with explicit dependence on the schedule-dependent weighting factors. Second, for overparameterized two-layer ReLU networks, we develop a Neural Tangent Kernel analysis tailored to diffusion training with stochastic gradients, yielding score-approximation error bounds along the SGD trajectory. Finally, our analysis quantifies the role of the reweighting factor in the score approximation error, providing theoretical guidance for weighting choices used in practice.

stat.ML↗

arXiv2026

Non-Asymptotic Error Bounds for SMC with Biased Proposals: Application to Conditional Diffusion Sampling

Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow. This paper develops a non-asymptotic error analysis for such SMC samplers. Under forward-smoothing forgetting conditions, we decompose the total error into a kernel bias, measuring the effect of replacing the ideal transition kernels by approximate ones, and a finite-particle Monte Carlo error. Our approach relies on extending local Doeblin-type conditions and Lyapunov drift arguments for Markov kernels to conditional distributions, thereby enabling a principled control of the bias. We then instantiate this general framework for conditional sampling with score-based diffusion models, and derive the first non-asymptotic error bound that jointly controls initialization error, time discretization, and score approximation in the reverse diffusion dynamics as well as finite-particle Monte Carlo error.

stat.ML↗

arXiv2026

On Forgetting and Stability of Score-based Generative models

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging stability and forgetting properties of the Markov chain associated with the reverse-time dynamics. Under weak assumptions, we provide the two structural properties to ensure the propagation of initialization and discretization errors of the backward process: a Lyapunov drift condition and a Doeblin-type minorization condition. A practical consequence is quantitative stability of the sampling procedure, as the reverse diffusion dynamics induces a contraction mechanism along the sampling trajectory. Our results clarify the role of stochastic dynamics in score-based models and provide a principled framework for analyzing propagation of errors in such approaches.

stat.ML↗

arXiv2025

Wasserstein Convergence of Critically Damped Langevin Diffusions

Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications and benefit from strong theoretical guarantees. Recently, methods inspired by statistical mechanics, in particular, Hamiltonian dynamics, have introduced Critically-damped Langevin Diffusions (CLDs), which define diffusion processes on extended spaces by coupling the data with auxiliary variables. These approaches, along with their associated score-matching and sampling procedures, have been shown to outperform standard diffusion-based samplers numerically. In this paper, we analyze a generalized dynamic that extends classical CLDs by introducing an additional hyperparameter controlling the noise applied to the data coordinate, thereby better exploiting the extended space. We further derive a novel upper bound on the sampling error of CLD-based generative models in the Wasserstein metric. This additional hyperparameter influences the smoothness of sample paths, and our discretization error analysis provides practical guidance for its tuning, leading to improved sampling performance.

math.ST↗

arXiv2024

An analysis of the noise schedule for score-based generative models

Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target.Recent literature has focused extensively on assessing the error between the target and estimated distributions, gauging the generative quality through the Kullback-Leibler (KL) divergence and Wasserstein distances. Under mild assumptions on the data distribution, we establish an upper bound for the KL divergence between the target and the estimated distributions, explicitly depending on any time-dependent noise schedule. Under additional regularity assumptions, taking advantage of favorable underlying contraction mechanisms, we provide a tighter error bound in Wasserstein distance compared to state-of-the-art results. In addition to being tractable, this upper bound jointly incorporates properties of the target distribution and SGM hyperparameters that need to be tuned during training. Finally, we illustrate these bounds through numerical experiments using simulated and CIFAR-10 datasets, identifying an optimal range of noise schedules within a parametric family.

math.ST↗