Conditioning Degenerate Diffusion Models
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define approximate loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, `a la "Ust"unel.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 13 of its 35 references that are in the map. First posted on arXiv 3 Sep 2026.
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13 of 35 references.
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- 2025Malliavin Calculus for Score-based Diffusion Models21 Mar
- 2024Conditioning non-linear and infinite-dimensional diffusion processes2 Feb
- 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
- 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
- 2022Riemannian Score-Based Generative Modelling6 Feb
- 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
Other references · 7
- 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,503
- 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
- 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
- 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 233
- 2019Theoretical guarantees for sampling and inference in generative models with latent diffusionscited by 97
- 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 29
- 2025Conditioning Diffusions Using Malliavin Calculuscited by 15
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- 2022An optimal control perspective on diffusion-based generative modeling
- 2026A Plug-in Interpretation of Conditioning in Score-Based Diffusion Models
- 2026Some remarks on the connection between generative diffusion and optimal transport
- 2026A unified perspective on fine-tuning and sampling with diffusion and flow models
- 2026Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach
- 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
- 2025Is RL fine-tuning harder than regression? A PDE learning approach for diffusion models
- 2026Barron Optimal Transport I: Generative Modeling