Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis
Diffusion models overcome bottlenecks in classical score-based samplers by using Gaussian distributions to establish convergence bounds. They achieve a sampling error of O(√dλmax log N/N), which is superior to unadjusted Langevin dynamics that suffer from an additional √κ factor due to conditioning. This shows that time-dependent scores effectively remove condition number dependence during sampling.