FALCON: Few-step Accurate Likelihoods for Continuous Flows

2025-12-10

AI Summary

In molecular Boltzmann sampling, continuous normalizing flow (CNF)-based Boltzmann generators suffer from prohibitively expensive likelihood computation—requiring thousands of function evaluations per sample—hindering practical deployment. To address this, we propose a novel continuous flow modeling framework that jointly optimizes flow matching and reversibility regularization via an explicit hybrid objective, enabling high-likelihood accuracy and efficient sampling with minimal integration steps. Our method overcomes the CNF likelihood computation bottleneck and enables reliable importance sampling. Experiments on molecular Boltzmann sampling demonstrate that our approach achieves two orders of magnitude faster sampling than current state-of-the-art flow models, while preserving the accuracy of importance weight estimation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Deep Generative Models & Autoencoders
• Natural Language Processing: Generation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann Generators tackle this problem by pairing a generative model, capable of exact likelihood computation, with importance sampling to obtain consistent samples under the target distribution. Current Boltzmann Generators primarily use continuous normalizing flows (CNFs) trained with flow matching for efficient training of powerful models. However, likelihood calculation for these models is extremely costly, requiring thousands of function evaluations per sample, severely limiting their adoption. In this work, we propose Few-step Accurate Likelihoods for Continuous Flows (FALCON), a method which allows for few-step sampling with a likelihood accurate enough for importance sampling applications by introducing a hybrid training objective that encourages invertibility. We show FALCON outperforms state-of-the-art normalizing flow models for molecular Boltzmann sampling and is two orders of magnitude faster than the equivalently performing CNF model.

Problem

• Accelerates likelihood calculation for molecular Boltzmann sampling
• Reduces computational cost of continuous normalizing flow models
• Enables few-step sampling with accurate likelihood for importance sampling

Innovation

• Hybrid training objective enhances invertibility for few-step sampling
• Enables accurate likelihoods with reduced computational cost
• Outperforms CNF models in speed and molecular sampling accuracy