Endpoint-Complete Diffusion Sampling via Log-SNR Boundary Closures

Modern fast diffusion samplers are typically designed as finite-interval integrators over a prescribed sequence of noise levels. This view reduces discretization error between neighboring nodes, but leaves a separate source of error at the two truncated ends of the sampling trajectory. We revisit diffusion sampling in log-SNR space, where the complete trajectory extends from the low-SNR limit $\lambda \to -\infty$ to the high-SNR limit $\lambda \to +\infty$. Taking these limits reveals an asymmetric boundary structure: the low-SNR endpoint admits a regular signal-prediction closure, whereas the high-SNR endpoint admits a regular noise-prediction closure. Motivated by this asymmetry, we propose endpoint-complete diffusion sampling, which keeps the interior solver unchanged and replaces only the first and last updates with endpoint-specific boundary plug-ins: DPM-FS and DPM-LS. We further connect the same endpoint asymmetry to generalized velocity prediction and show that, under variance normalization, EDM-style residual preconditioning maps non-degenerate linear targets to the same generalized velocity direction up to sign. Experiments on CIFAR-10, AFHQv2, FFHQ, and ImageNet demonstrate improved few-step sampling quality.