arXiv cs.AI· Bingyan Han·· 11 小时前AI 评分31
Volterra 生成模型：通过马尔可夫提升实现更灵活的时间依赖
Volterra Generative Models via Markovian Lifting
AI 导读
研究者提出 Volterra 生成模型，用马尔可夫近似处理 Volterra 过程的非马尔可夫结构，使去噪问题经高斯条件化后回到原始数据维度，并可与 variance-exploding、variance-preserving 表示建立联系。
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