Tail-Index Annealing for Long-Tailed Diffusion Models

Classical denoising diffusion models rely on Gaussian noise throughout the forward process. Recent stable-noise diffusion models, such as the Denoising Lévy Probabilistic Model (DLPM), replace it with stable noise that has a single fixed tail index, forcing a fixed compromise between terminal initialization and reverse estimation. Direct substitution of a time-varying tail index into DLPM fails since increments with different indices do not form a single stable law. We introduce **Annealed DLPM** (A-DLPM), a consistent framework that increases the tail index along a half-cosine forward schedule and traverses the reverse schedule during generation. We construct the corresponding conditional Gaussian reverse kernel, which reduces to the original DLPM when the tail index is fixed. The resulting annealed residual admits an exact, interpretable spectral-curvature characterization. On two-dimensional data, A-DLPM attains the lowest mean tail-sensitive error among evaluated methods; on long-tailed image benchmarks, it attains the highest mean Recall among all evaluated methods and improves both FID and Recall over the evaluated DLPM, DLIM, and Gaussian DDPM controls.