Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Training

Antonio Ocello tests the idea that heavy-tailed noise improves diffusion and flow-based generative models by matching heavy-tailed data and encouraging diverse samples. Replacing Gaussian noise also changes the estimation task. A combined theoretical and experimental study derives sampling-error bounds for representative heavy- and light-tailed diffusion models, finding that heavy-tailed noise makes statistical estimation harder and produces less favourable bounds. Experiments with synthetic and real data recover the predicted trade-off. The results question whether heavy-tailed initialization reliably improves exploration of rare regions. This is joint work with Hamza Cherkaoui and Hélène Halconruy.