Active Flow Matching

Yashvir S. Grewal; Daniel M. Steinberg; Thang D. Bui; Cheng Soon Ong; Edwin V. Bonilla

cs.LGMar 1, 2026

Active Flow Matching

Authors: Yashvir S. Grewal, Daniel M. Steinberg, Thang D. Bui, Cheng Soon Ong, Edwin V. Bonilla

Organizations: School of Computing, College of Systems and Society, Australian National University, Australia · Data61, CSIRO, Australia

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.

Figures & tables

Panel of Figure 1 — Figure 1: Budget-constrained optimisation on Ehrlich synthetic landscapes and the AAV capsid design task. We report the simple regret

Panel of Figure 2 — Figure 2: Structure-based protein design with FoldX oracles. We plot the best score found vs. oracle calls;

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Generative Flow & Classifier Architecture
Parameter	Value / Schedule
Architecture	Bi-LSTM
Hidden Dimension	$256$
Embedding Dimension	$128$
Layers	$3$
Dropout	$0.1$

Appendix

Table 1: Hyperparameters and dynamic scheduling for Ehrlich experiments.

Parameter	Value / Schedule
Mixing Coefficients (Round $r$ )
Replay ( $\alpha_{\mathrm{rb}}$ )	$0.3$ (fixed)
Flow ( $\alpha_{\mathrm{flow}}$ )	$(1-\alpha_{\mathrm{rb}})\times 0.15$ ( $r<5$ )
	$(1-\alpha_{\mathrm{rb}})\times 0.35$ ( $r\geq 5$ )
Prior ( $\alpha_{0}$ )	$1-\alpha_{\mathrm{rb}}-\alpha_{\mathrm{flow}}$
Buffer Temp ( $\gamma$ )	$0.2$

Appendix

Table 2: Hyperparameters for FoldX experiments. Unlisted parameters match Table 1 .

Generative Flow Model
Parameter	Value / Schedule
Architecture	Transformer
Layers	$5$
Heads	$8$
Hidden Dim	$256$
Dropout	$0.1$

Appendix

Table 3: Hyperparameters for AAV Capsid Optimisation.

Generative Flow Model
Parameter	Value / Schedule
Architecture	Bi-LSTM
Hidden Dimension	$512$
Embedding Dimension	$256$
Layers	$4$
Dropout	$0.1$

Appendix

Table 4: Hyperparameters for Dockstring (F2/Thrombin) experiments.

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Flow Matching Generative Modeling Continuous Normalizing Flows Flow-Based Generative Modeling

Open paper AskPDF arXiv

Flow Matching (FM) is a simulation-free method for learning a continuous, invertible flow that interpolates between two distributions, and in particular generates data from noise. Inspired by the variational nature of the diffusion process as a gradient flow, we introduce a stepwise FM model, Local Flow Matching (LFM), which sequentially learns a sequence of FM submodels, each matching a diffusion process up to the time-step size in the data-to-noise direction. In each step, the two distributions to be interpolated by the sub-flow model are closer than those in the full-flow matching model, which interpolates data to noise distributions, enabling smaller models with more efficient training. This variational perspective also allows us to prove a theoretical generation guarantee for the proposed flow model in terms of the

χ^2

-divergence between the generated and true data distributions, leveraging the contraction property of the diffusion process. In practice, the stepwise structure of LFM is naturally amenable to model distillation, and various distillation techniques can be applied to accelerate generation. We empirically demonstrate that LFM achieves competitive generative performance compared to FM on unconditional generation of tabular and image datasets, and on conditional generation of robotic manipulation policies.

Abstract

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