流控与融合的统一密度算子视角
A Unified Density Operator View of Flow Control and Merging
AI总结：
本文提出了一种统一的概率空间框架，通过奖励引导的流融合方法，实现流控与融合的统一处理，并在分子设计和构象生成中展示了其应用。
摘要：
大规模流和扩散模型的最新进展引发了两个根本性的算法挑战：(i) 基于控制的奖励适应预训练流，以及 (ii) 多个模型的整合，即流融合。尽管当前方法分别解决这些问题，我们引入了一个统一的概率空间框架，该框架将两者作为极限情况包含在内，并使奖励引导的流融合成为可能，从而允许在任务意识下合理地组合多个预训练流（例如在最大化药物发现效用的同时融合先验）。我们的公式使在生成模型密度上表达丰富的运算家族成为可能，包括交集（例如，以强制安全）、并集（例如，以组合多样化模型）、插值（例如，用于发现），以及它们的奖励引导的对应物，以及通过生成电路实现复杂逻辑表达式。接下来，我们介绍奖励引导的流融合（RFM），一种镜像下降方案，它将奖励引导的流融合减少为一系列标准微调问题。然后，我们通过RFM提供了奖励引导和纯流融合的首次理论保证。最后，我们展示了所提出方法在示例设置中的能力，提供了可解释的视觉见解，并将我们的方法应用于高维de-novo分子设计和低能构象生成。
英文摘要：
Recent progress in large-scale flow and diffusion models raised two fundamental algorithmic challenges: (i) control-based reward adaptation of pre-trained flows, and (ii) integration of multiple models, i.e., flow merging. While current approaches address them separately, we introduce a unifying probability-space framework that subsumes both as limit cases, and enables reward-guided flow merging, allowing principled, task-aware combination of multiple pre-trained flows (e.g., merging priors while maximizing drug-discovery utilities). Our formulation renders possible to express a rich family of operators over generative models densities, including intersection (e.g., to enforce safety), union (e.g., to compose diverse models), interpolation (e.g., for discovery), their reward-guided counterparts, as well as complex logical expressions via generative circuits. Next, we introduce Reward-Guided Flow Merging (RFM), a mirror-descent scheme that reduces reward-guided flow merging to a sequence of standard fine-tuning problems. Then, we provide first-of-their-kind theoretical guarantees for reward-guided and pure flow merging via RFM. Ultimately, we showcase the capabilities of the proposed method on illustrative settings providing visually interpretable insights, and apply our method to high-dimensional de-novo molecular design and low-energy conformer generation.
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