Conditional Particle Matching: State-Conditioned Particle Fields for Few-step Generation

Drifting Models train generators by moving their endpoint pushforwards toward the data distribution, while Drift Flow Matching extends this principle to time-indexed marginal transports. Marginal matching alone, however, does not uniquely determine how clean predictions depend on a particular noisy state: distinct reverse kernels can induce the same clean marginal. We introduce Conditional Particle Matching (CPM), a population conditional reverse-KL formulation that targets the corruption posterior $p(x_0\mid x_t,t,c)$ with a stochastic reverse kernel ${\rho }_{\theta }(x_0\mid x_t,t,c)$. This stochastic family can, in principle, represent multiple clean explanations of the same corrupted state. At the population level, the conditional reverse-KL field decomposes into a data-prior term, an analytic likelihood term from the known corruption process, and a state-conditioned model self-field. Guided by this decomposition, we develop a practical feature-space particle semi-gradient built on the released Drifting implementation. CPM operates in clean-endpoint coordinates: frozen perceptual features act exclusively on clean-coordinate predictions and references, while the practical update incorporates explicit noisy-state dependence through the analytic corruption likelihood and an SNR-dependent normalized distance in native latent space. The formulation further motivates fixed-state sampling and observation-shuffle controls to probe conditional behavior that pooled distributional metrics alone cannot reveal.