FUND: Density Flow for Sampling Unnormalised Distributions
cs.LG, hep-lat
Submitted: 2026-09-26
Updated: 2026-09-26
Comments: 24 pages, 6 figures
Journal ref: Transactions on Machine Learning Research, 2026
License: http://creativecommons.org/licenses/by/4.0/
The gist: Efficient sampling from Boltzmann distributions is central to modelling complex physical systems.
Terminology
Abstract
Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar ϕ 4 theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.
Sources
- SCORENF: Score-based Normalizing Flows for Sampling Unnormalized distributions
- Continual Learning: Tackling Catastrophic Forgetting in Deep Neural Networks with Replay Processes
Related papers
- Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
- AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
- Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
- Convergence issues in Relational Concept Analysis based on AOC-posets
- Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding
- Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks