用数学变换构建无限维生成扩散模型，更灵活且理论严谨。
Infinite-dimensional generative diffusions via Doob's h-transform
- 通过测度变换让参考扩散过程指向目标分布
- 在无限维空间中实现稳定生成，理论可验证
- 适合研究高维生成模型的理论工作者
本文提出一种基于杜布 h 变换的严格框架，用于在无限维空间定义生成扩散模型。与依赖去噪过程时间反转的方法不同，该方法通过指数测度变换，将参考扩散过程强制导向目标分布。相较于现有方法，该框架天然适用于无限维设置，具备更强的灵活性。理论推导在可验证条件下完成，并建立了相对于目标测度的误差界。我们证明，在变换测度下的强制过程可通过最小化得分匹配目标进行近似，并在合成数据和真实数据上验证了方法的有效性。
原文摘要 · Abstract (English)
This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform. Rather than relying on time reversal of a noising process, a reference diffusion is forced towards the target distribution by an exponential change of measure. Compared to existing methodology, this approach readily generalises to the infinite-dimensional setting, hence offering greater flexibility in the diffusion model. The construction is derived rigorously under verifiable conditions, and bounds with respect to the target measure are established. We show that the forced process under the changed measure can be approximated by minimising a score-matching objective and validate our method on both synthetic and real data.
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