Volterra Generative Models

The article introduces Volterra generative models, a novel framework for score-based diffusion that incorporates path-dependent noise using fractional kernels, addressing the limitations of traditional Brownian perturbations. It employs finite-dimensional Markovian lifts and a Gaussian-bridge reconstruction sampler to manage non-Markovian dynamics, demonstrating improved performance on benchmark datasets like MNIST and CIFAR-10. This advancement is significant for practitioners as it offers a method to enhance generative model stability and output quality in complex image generation tasks.