Speaker
Description
Near criticality, the correlation length becomes large, so a generative model trained from unstructured Gaussian noise must learn both infrared physics and ultraviolet fluctuations. We propose an inverse-blocking strategy that separates these tasks: coarse configurations provide the long-distance structure, while a local transported-detail normalizing flow proposes the missing fine degrees of freedom. The coarse action and the flow are used as proposal mechanisms, with patchwise Metropolis--Hastings updates targeting the full fine-theory distribution.
We test this method in two-dimensional $\phi^4$ theory using a small-stencil blocking kernel and local conditional flows. The method gives stable $8\to 16$ and $16 \to 32$ upscaling, with comparable acceptance and logweight behavior across volumes. We study patch size, latent update cadence, many-short-chain strategies, initial-state diagnostics, and burn-in effects. These tests show that renormalization-guided coarse-to-fine generation can reduce the burden on the learned model while retaining exact correction through the target action.