Deep generative models, particularly diffusion models, have achieved remarkable success but face significant challenges when trained on real-world, long-tailed datasets-where few "head" classes dominate and many "tail" classes are underrepresented. This paper develops a theoretical framework for long-tailed learning via diffusion models through the lens of deep mutual learning. We introduce a novel regularized training objective that combines the standard diffusion loss with a mutual learning term, enabling balanced performance across all class labels, including the underrepresented tails. Our approach to learn via the proposed regularized objective is to formulate it as a multi-player game, with Nash equilibrium serving as the solution concept. We derive a non-asymptotic first-order convergence result for individual gradient descent algorithm to find the Nash equilibrium.

Meanwhile, there are a handful of results[44,25]thataimatunderstanding differentfacetsofthetraining process.