Heavy-tailed denoising score matching
This work addresses a domain-specific problem for researchers in generative modeling by providing an incremental improvement over existing methods.
The paper tackled the limitations of Gaussian noise in score-based generative models by extending denoising score-matching to heavy-tailed distributions, resulting in improved score estimation, controllable sampling convergence, and more balanced generative performance for imbalanced datasets.
Score-based model research in the last few years has produced state of the art generative models by employing Gaussian denoising score-matching (DSM). However, the Gaussian noise assumption has several high-dimensional limitations, motivating a more concrete route toward even higher dimension PDF estimation in future. We outline this limitation, before extending the theory to a broader family of noising distributions -- namely, the generalised normal distribution. To theoretically ground this, we relax a key assumption in (denoising) score matching theory, demonstrating that distributions which are differentiable almost everywhere permit the same objective simplification as Gaussians. For noise vector norm distributions, we demonstrate favourable concentration of measure in the high-dimensional spaces prevalent in deep learning. In the process, we uncover a skewed noise vector norm distribution and develop an iterative noise scaling algorithm to consistently initialise the multiple levels of noise in annealed Langevin dynamics (LD). On the practical side, our use of heavy-tailed DSM leads to improved score estimation, controllable sampling convergence, and more balanced unconditional generative performance for imbalanced datasets.