← 研踪 PaperTrailarXiv:2606.18071 · v2
Volterra Generative Models via Markovian Lifting
首次提交 2026-06-16 23:40
版本更新 2026-11-05 08:40
雷达观测 2026-11-06 11:06
摘要
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.
作者备注：Substantially revised manuscript; author list updated; 35 pages
观测到的版本
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v2 · 2026-11-05 08:40 · 最新观测版本
Volterra Generative Models via Markovian Lifting
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.
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