# Active Flow Matching

arXiv: https://arxiv.org/abs/2603.00877 · HTML: https://mlsanity.com/paper/2603.00877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 6 of 6)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Design by adaptive sampling](https://mlsanity.com/paper/1810.03714/) (2018)
- [Closed-Form Test Functions for Biophysical Sequence Optimization Algorithms](https://mlsanity.com/paper/2407.00236/) (2024)
- [Amortized Active Generation of Pareto Sets](https://mlsanity.com/paper/2510.21052/) (2025)

## Abstract (arXiv)

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.