统一生成模型为路径积分，揭示各类模型的共同数学本质。
Unifying Generative Models with Path Integrals
- 将生成模型统一为路径积分框架，不同模型对应不同求解方式。
- 一阶修正使确定性采样误差从53%降至1.6%，无需额外随机采样成本。
- 适用于希望理解生成模型统一理论的研究者，尤其关注模型设计与优化。
我们将生成建模表述为路径积分，其中基于流、扩散、变分和对抗的模型均源于同一主作用量的不同求解原则。其Martin-Siggia-Rose-Janssen-de Dominicis（MSRJD）形式将自由概率流与相互作用概率流分离，使其可应用图示微扰论。展开后得到确定性采样的一阶修正，在无随机采样代价下实现性能提升：在可解和非线性漂移场景中，将树级误差从53%降至1.6%。学习到的不完美得分以插入项形式出现，导出响应加权的得分匹配目标；对称性等价漂移设计则转化为带有有效场论幂次计数的算子展开。
原文摘要 · Abstract (English)
We formulate generative modeling as a path integral in which flow-based, diffusion-based, variational, and adversarial models arise as different evaluation principles for a single master action. Its Martin-Siggia-Rose-Janssen-de~Dominicis (MSRJD) form separates free from interacting probability flows and opens them to diagrammatic perturbation theory. The expansion yields a one-loop correction to deterministic samplers at no stochastic-sampling cost, which we validate on solvable and nonlinear drifts, where it reduces a 53 % tree-level error to 1.6 %. Imperfect learned scores enter as insertions and yield a response-weighted score-matching objective, and symmetry-equivariant drift design becomes an operator expansion with EFT power counting.
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