Volterra 生成模型：基于 Markovian Lifting 的方法研究
Volterra Generative Models via Markovian Lifting
AI 导读
论文提出 Volterra 生成模型，用 Markovian Lifting 提供马尔可夫近似，解决 Volterra 过程非马尔可夫结构带来的 score 学习与逆时模拟难题。
正文 · 原文
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.
| Comments: | Substantially revised manuscript; author list updated; 35 pages |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.18071 [cs.LG] |
| (or arXiv:2606.18071v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.18071 arXiv-issued DOI via DataCite |
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)
来源：arXiv cs.AI · arxiv.org