Active Flow Matching

TL;DR

Active Flow Matching (AFM) introduces a novel approach that reformulates flow models to enable gradient-based optimization for high-fitness regions, effectively integrating with variational frameworks for online design tasks.

Contribution

AFM reformulates variational objectives for flow models, allowing gradient-based steering towards high-fitness regions while maintaining compatibility with variational search methods.

Findings

AFM performs competitively on protein and small molecule design tasks.

AFM demonstrates effective exploration-exploitation under limited experimental budgets.

The method successfully integrates flow models with variational objectives.

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.