[Submitted on 16 Jun 2026 (v1), last revised 5 Nov 2026 (this version, v2)]
Abstract:Diffusion-based generative models usually perturb data through Markov processes driven by Brownian motion. Volterra processes allow more flexible temporal dependence, but their non-Markovian structure complicates score learning and reverse-time simulation. We develop Volterra generative models and provide Markovian approximations. Gaussian conditioning then reduces the denoising problem to the original data dimension. We present the connections with variance-exploding and variance-preserving representations. Our framework also permits reuse of pretrained denoisers such as EDM2 networks. With one auxiliary factor, our models trained from scratch achieve FIDs of $0.547$ on MNIST and $1.860$ on conditional CIFAR-10. With autoguidance, ImageNet64 FID reaches $1.912$ after fine-tuning, while ImageNet512 FID reaches $1.903$ using frozen pretrained networks.
Submission history
From: Bingyan Han [view email]
[v1] Tue, 16 Jun 2026 15:40:09 UTC (1,442 KB)
[v2] Thu, 5 Nov 2026 00:40:07 UTC (18,517 KB)
