VP vs VE Comparison

Key Insight

VP and VE are the two classic ways to define the forward noising process of a diffusion model. Variance-Preserving (VP) — the family DDPM belongs to — shrinks the original signal as it adds noise so the total variance stays around 1 the whole way; Variance-Exploding (VE) — used by the original score-based papers — leaves the signal untouched and just piles on ever-larger noise, so the variance grows without bound. The two are mathematically interconvertible and reach similar FID, but they differ in numerical conditioning and in which samplers behave well, which is exactly what makes the comparison instructive. This project trains the same model under both SDE families and compares quality, training stability, and sampler behavior side by side.