Generative Modeling with Probability-Preserving Dynamics

Modern generative modeling usually produces samples by transporting a simple noise prior to the data distribution. We study a complementary setting: once a useful state already exists, can a pretrained flow be reused as a stochastic transition rather than restarted from noise? We construct two reusable kernels directly from pretrained flow checkpoints, without retraining: a denoiser-based Metropolis kernel (dMALA), whose ideal target is the Gaussian-smoothed law $p_{\sigma }$, and a predictor–corrector kernel whose ideal target is $p$. We also characterize how one-step model and numerical errors accumulate under a local contraction assumption. On ImageNet-256, dMALA repairs deliberately weak generated states from FID $10.70$ to $3.19$ while retaining high similarity to the input (DINO $0.80$). The same dynamics also support controlled variation: as the chain length increases, samples move progressively farther from their inputs, providing a controllable transition from local variation to broader exploration. Experiments on a synthetic Swiss-roll target, ImageNet-256, and Oxford Flowers-102 show that these dynamics can reuse existing flow models when a useful initial state is already available.