2025/04/25 by Ilin, Vasily, Peter V. Sushko, Jingwei Hu +2 · 2 citations
Computer Science · Mathematics · #35Q84 #49Q22 #68T07 #FOS: Computer and information sciences #FOS: Mathematics #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Markov Chains and Monte Carlo Methods #Primary 65C05 #Probability (math.PR) #Secondary 60H10 #Statistics Theory (math.ST) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2504.18130
openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL(ft‖π) by learning the time-varying score ∇ log ft on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.