aiqbench analysis
This research introduces ScoreNF, a score-based learning framework that combines Normalizing Flows with Independent Metropolis-Hastings sampling to efficiently handle unnormalized distributions common in physics and complex systems. By reducing reliance on large datasets and expensive MCMC training data, the method offers a robust alternative for addressing mode collapse and slow convergence issues in high-dimensional modeling tasks.
SCORENF: Score-based Normalizing Flows for Sampling Unnormalized distributions
arXiv:2510.21330v2 Announce Type: replace Abstract: Unnormalized probability distributions are central to modeling complex physical systems across various scientific domains. Traditional sampling methods, such as Markov Chain Monte Carlo (MCMC), often suffer from slow convergence, critical slowing down, poor mode mixing, and high autocorrelation. In contrast, likelihood-based and adversarial machine learning models, though effective, are heavily data-driven, requiring large datasets and often encountering mode covering and mode collapse. In this work, we propose ScoreNF, a score-based learning framework built on the Normalizing Flow (NF) architecture, integrated with an Independent Metropolis-Hastings (IMH) module, enabling efficient and unbiased sampling from unnormalized target distributions. We show that ScoreNF maintains high performance even with small training ensembles, thereby reducing reliance on computationally expensive MCMC-generated training data. We also present a method for assessing mode-covering and mode-collapse behaviours. We validate our method on synthetic 2D distributions (MOG-4 and MOG-8) and the high-dimensional $\phi^4$ lattice field theory distribution, demonstrating its effectiveness for sampling tasks.
Abstract:Unnormalized probability distributions are central to modeling complex physical systems across various scientific domains. Traditional sampling methods, such as Markov Chain Monte Carlo (MCMC), often suffer from slow convergence, critical slowing down, poor mode mixing, and high autocorrelation. In contrast, likelihood-based and adversarial machine learning models, though effective, are heavily data-driven, requiring large datasets and often encountering mode covering and mode collapse. In this work, we propose ScoreNF, a score-based learning framework built on the Normalizing Flow (NF) architecture, integrated with an Independent Metropolis-Hastings (IMH) module, enabling efficient and unbiased sampling from unnormalized target distributions. We show that ScoreNF maintains high performance even with small training ensembles, thereby reducing reliance on computationally expensive MCMC-generated training data. We also present a method for assessing mode-covering and mode-collapse behaviours. We validate our method on synthetic 2D distributions (MOG-4 and MOG-8) and the high-dimensional $\phi^4$ lattice field theory distribution, demonstrating its effectiveness for sampling tasks.
\c{opyright} 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works
Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)
arXiv:2510.21330 [cs.LG]
(or arXiv:2510.21330v2 [cs.LG] for this version)
https://doi.org/10.1109/ICASSP55912.2026.11463153 DOI(s) linking to related resources
Full text under the publisher's open licence · 237 words
Related coverage
SIMANF: Sample Free Learning of Unnormalized Distributions via Simulated Annealing in Normalizing Flows
arXiv · Sep 30, 2026
Inference meta-monitoring for Amazon SageMaker AI endpoints with Amazon Quick
AWS · Jul 30, 2026
Building and evaluating model diffing agents
AI Alignment Forum · Jun 12, 2026
Debugging Logprob Mismatches in LLM Reinforcement Learning
AMD · Sep 23, 2026