# Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplers

arXiv: https://arxiv.org/abs/2603.19670 · HTML: https://mlsanity.com/paper/2603.19670/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 27 of its 43 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [KL Convergence Guarantees for Score diffusion models under minimal data assumptions](https://mlsanity.com/paper/2308.12240/) (2023)
- [Optimal score estimation via empirical Bayes smoothing](https://mlsanity.com/paper/2402.07747/) (2024)
- [Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models](https://mlsanity.com/paper/2311.11003/) (2023)
- [Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances](https://mlsanity.com/paper/2401.17958/) (2024)
- [O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions](https://mlsanity.com/paper/2409.18959/) (2024)
- [Low-dimensional adaptation of diffusion models: Convergence in total variation](https://mlsanity.com/paper/2501.12982/) (2025)
- [Non-asymptotic bounds for sampling algorithms without log-concavity](https://mlsanity.com/paper/1808.07105/) (2018)
- [Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance](https://mlsanity.com/paper/2501.02298/) (2025)
- [Provable Acceleration for Diffusion Models under Minimal Assumptions](https://mlsanity.com/paper/2410.23285/) (2024)
- [Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance](https://mlsanity.com/paper/2508.03210/) (2025)
- [Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration](https://mlsanity.com/paper/2502.04849/) (2025)
- [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026)
- [Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients](https://mlsanity.com/paper/2505.03432/) (2025)
- [Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers](https://mlsanity.com/paper/2410.14237/) (2024)
- [Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions](https://mlsanity.com/paper/2402.08082/) (2024)
- [Wasserstein Bounds for generative diffusion models with Gaussian tail targets](https://mlsanity.com/paper/2412.11251/) (2024)
- [Non-asymptotic error bounds for probability flow ODEs under weak log-concavity](https://mlsanity.com/paper/2510.17608/) (2025)
- [On Forgetting and Stability of Score-based Generative models](https://mlsanity.com/paper/2601.21868/) (2026)

## Built on by (most cited first, 1 of 1)

- [Universal Local Error and Realized Amplification for the First-Order EDM Predictor](https://mlsanity.com/paper/2610.10190/) (2026)

## Abstract (arXiv)

Many Wasserstein analyses of diffusion samplers control reverse-time propagation by global stability summaries of the learned drift. These summaries can hide radial geometry: equal-height expansive regions of different width can yield different propagation costs. We give a profile-adapted propagation interface for scalar-isotropic reverse-SDE windows with certified learned-drift profiles. A certified lower radial profile is compiled into an affine-tail transportation cost: reflection coupling reduces stability to a one-dimensional slope budget, and Hardy capacity quantifies the load paid before a contractive tail reserve. The compiler yields an adapted cost, contraction rate, and retained tail slope. Score-modeling and solver residuals are treated as forcing inputs and propagate additively in the adapted Wasserstein distance. Quadratic Wasserstein error is reported only at terminal time, using the retained tail slope with tail, moment, or support information. Gaussian-smoothed denoising geometry supplies inverse-radius profiles for uniformly dissipative, bounded-amplitude, and common-covariance mixture windows. Fixed-height examples show that adverse height, even with eventual reserve, does not determine the certificate; barrier examples show that the load dependence is structural.