# A Unified Approach to Analysis and Design of Denoising Markov Models

arXiv: https://arxiv.org/abs/2504.01938 · HTML: https://mlsanity.com/paper/2504.01938/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2025.

## Built on by (most cited first, 12 of 12)

- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spaces](https://mlsanity.com/paper/2506.07903/) (2025)
- [MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Control](https://mlsanity.com/paper/2508.10684/) (2025)
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- [SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogate](https://mlsanity.com/paper/2605.18745/) (2026)
- [A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fields](https://mlsanity.com/paper/2505.13189/) (2025)
- [Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction](https://mlsanity.com/paper/2512.05092/) (2025)
- [Simple Approximation and Derivative Free Inference-Time Scaling for Diffusion Models via Sequential Monte Carlo on Path Measures](https://mlsanity.com/paper/2605.17850/) (2026)
- [Free energy Estimation on Any State Space](https://mlsanity.com/paper/2605.31063/) (2026)
- [Multi-Mask Diffusion Language Models for Few-Step Generation](https://mlsanity.com/paper/2607.19686/) (2026)
- [FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models](https://mlsanity.com/paper/2609.35947/) (2026)
- [From Global to Tail Convergence: Dynamics of α-Stable Score-Based Generative Models](https://mlsanity.com/paper/2610.19773/) (2026)

## Abstract (arXiv)

Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic design choices and theoretical analysis. In this paper, we aim to establish a rigorous mathematical foundation for denoising Markov models, a broad class of generative models that postulate a forward process transitioning from the target distribution to a simple, easy-to-sample distribution, alongside a backward process particularly constructed to enable efficient sampling in the reverse direction. Leveraging deep connections with nonequilibrium statistical mechanics and generalized Doob's h-transform, we propose a minimal set of assumptions that ensure: (1) explicit construction of the backward generator, (2) a unified variational objective directly minimizing the measure transport discrepancy, and (3) adaptations of the classical score-matching approach across diverse dynamics. Our framework unifies existing formulations of continuous and discrete diffusion models, identifies the most general form of denoising Markov models under certain regularity assumptions on forward generators, and provides a systematic recipe for designing denoising Markov models driven by arbitrary L'evy-type processes. We illustrate the versatility and practical effectiveness of our approach through novel denoising Markov models employing geometric Brownian motion and jump processes as forward dynamics, highlighting the framework's potential flexibility and capability in modeling complex distributions.