用活性粒子的势场实现扩散生成模型，让活系统也能做生成式AI。
An effective potential for generative modelling with active matter
- 用有持续时间的活性粒子模拟扩散过程，通过反向时间施加有效势场生成数据。
- 在人工数据上验证有效势场可生成高质量样本，且仅依赖一阶持续时间近似。
- 为生物系统、活性物质中的生成建模提供新思路，适合物理启发的生成模型研究者。
基于分数的扩散模型通过反转扩散过程从复杂数据分布中生成样本，是当前生成式AI的主流方法。本文展示如何基于具有有限相关时间的活性粒子过程实现生成扩散模型。通过在位置坐标上施加随时间变化的有效势场，实现时间反演，该势场可直接用于模拟与实验，驱动活性涨落生成合成数据。该有效势场在持续时间的一阶近似下成立，其力场完全由标准得分函数及其二阶导数决定。针对人工数据分布的数值实验验证了该势场的有效性，为利用活性及生命系统中的涨落开展生成式人工智能研究开辟了新路径。
原文摘要 · Abstract (English)
Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion model can be implemented based on an underlying active particle process with finite correlation time. Time reversal is achieved by imposing an effective time-dependent potential on the position coordinate, which can be readily implemented in simulations and experiments to generate new synthetic data samples driven by active fluctuations. The effective potential is valid to first order in the persistence time and leads to a force field that is fully determined by the standard score function and its derivatives up to 2nd order. Numerical experiments for artificial data distributions confirm the validity of the effective potential, which opens up new avenues to exploit fluctuations in active and living systems for generative AI purposes.
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