Active Flow Matching

2026-02-28

AI Summary

This work addresses the challenge of integrating discrete diffusion and flow matching models into online black-box optimization frameworks based on Variational Search Distributions (VSD) and Conditional adaptive Sampling (CbAS). To bridge this gap, the authors propose Active Flow Matching, which for the first time unifies flow matching with variational optimization by reformulating the variational objective over the conditional endpoint distribution along flow trajectories, enabling gradient-guided optimization. The method introduces an active guidance mechanism conditioned on endpoint distributions and derives self-normalized importance sampling estimators for both forward and reverse KL divergences. Evaluated on protein and small-molecule design tasks, the forward KL variant demonstrates superior or competitive exploration–exploitation balance under limited experimental budgets compared to current state-of-the-art approaches.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Active Learning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

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

Abstract

Discrete diffusion and flow matching models capture complex, non-additive and non-autoregressive structure in high-dimensional objective landscapes through parallel, iterative refinement. However, their implicit generative nature precludes direct integration with principled variational frameworks for online black-box optimisation, such as variational search distributions (VSD) and conditioning by adaptive sampling (CbAS). We introduce Active Flow Matching (AFM), which reformulates variational objectives to operate on conditional endpoint distributions along the flow, enabling gradient-based steering of flow models toward high-fitness regions while preserving the rigour of VSD and CbAS. We derive forward and reverse Kullback-Leibler (KL) variants using self-normalised importance sampling. Across a suite of online protein and small molecule design tasks, forward-KL AFM consistently performs competitively compared to state-of-the-art baselines, demonstrating effective exploration-exploitation under tight experimental budgets.

Problem

• flow matching
• black-box optimization
• variational inference
• online optimization
• generative modeling

Innovation

• Active Flow Matching
• variational search distributions
• conditioning by adaptive sampling
• flow matching
• online black-box optimization