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.

翻译：离散扩散与流匹配模型通过并行迭代优化，捕捉高维目标景观中复杂、非加性和非自回归的结构。然而，其隐式生成性质阻碍了与在线黑盒优化的原则性变分框架（如变分搜索分布和自适应采样条件化）的直接集成。本文提出主动流匹配，该方法将变分目标重新表述为沿流的条件端点分布上的操作，从而在保持变分搜索分布和自适应采样条件化严谨性的同时，实现基于梯度的流模型向高适应度区域的引导。我们利用自归一化重要性采样推导了前向与反向Kullback-Leibler变体。在一系列在线蛋白质与小分子设计任务中，前向Kullback-Leibler主动流匹配相较于最先进的基线方法始终表现出竞争力，证明了其在严格实验预算下有效的探索-利用平衡。