Infinite-dimensional generative diffusions via Doob's h-transform

• URL: http://arxiv.org/abs/2602.06621v1
• Date: Fri, 06 Feb 2026 11:25:32 GMT
• Title: Infinite-dimensional generative diffusions via Doob's h-transform
• Abstract summary: This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform.<n>We show that the forced process under the changed measure can be approximated by minimising a score-matching objective.
• Score: 0.6015898117103069
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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