Satoshi Iso

Lattice field theory usually judges generative samplers by effective sample size (ESS), a measure of overlap between generated and target samples, but a small global ESS need not mean inaccurate long-distance observables. A scale-resolved overlap diagnostic shows that small errors spread over many short-distance modes can dominate ESS; in two-dimensional φ⁴ theory near criticality, trained diffusion samplers show path-weight ESS fractions falling rapidly with volume while low moments of the magnetization stay close to benchmark values. Given the target marginal, a Metropolis test on a few collective variables keeps an acceptance rate of order one in the tests, and exact local updates then reduce the remaining mismatch.

Lattice field theory usually judges generative samplers by effective sample size (ESS), a measure of overlap between generated and target samples, but a small global ESS need not mean inaccurate long-distance observables. A scale-resolved overlap diagnostic shows that small errors spread over many short-distance modes can dominate ESS; in two-dimensional φ⁴ theory near criticality, trained diffusion samplers show path-weight ESS fractions falling rapidly with volume while low moments of the magnetization stay close to benchmark values. Given the target marginal, a Metropolis test on a few collective variables keeps an acceptance rate of order one in the tests, and exact local updates then reduce the remaining mismatch.