# A Generalized McDiarmid Inequality: Sample Reuse and Non-Uniform Unbounded Differences

arXiv: https://arxiv.org/abs/2610.17159 · HTML: https://mlsanity.com/paper/2610.17159/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [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)
- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)
- [A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models](https://mlsanity.com/paper/2408.02320/) (2024)
- [Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models](https://mlsanity.com/paper/2311.11003/) (2023)
- [Linear Convergence of Diffusion Models Under the Manifold Hypothesis](https://mlsanity.com/paper/2410.09046/) (2024)
- [Improved Convergence of Score-Based Diffusion Models via Prediction-Correction](https://mlsanity.com/paper/2305.14164/) (2023)
- [Concentration in unbounded metric spaces and algorithmic stability](https://mlsanity.com/paper/1309.1007/) (2013)
- [Score-based generative models are provably robust: an uncertainty quantification perspective](https://mlsanity.com/paper/2405.15754/) (2024)
- [An extension of McDiarmid's inequality](https://mlsanity.com/paper/1511.05240/) (2015)

## Abstract (arXiv)

We develop a novel generalization of McDiarmid's concentration inequality and use it to obtain a uniform law of large numbers result and error bounds on stochastic optimization problems which simultaneously incorporate two key features: 1) They capture the benefit of training sample reuse in algorithms that also employ easily-sampled auxiliary random variables. 2) They allow for one-component mean-difference bounding functions which are both unbounded in the component of interest and have non-uniform dependence on another component. We demonstrate the utility of our method by deriving concentration inequalities for score-based generative modeling. This application naturally leverages both key features of our new tools: 1) It utilizes auxiliary Gaussian random variables in conjunction with the training samples; accounting for training sample reuse results in tighter error bounds by effectively integrating out the dependence on the auxiliary random variables. 2) The ability to handle non-uniform mean-difference bounding functions allows us to treat unbounded score models and data distributions with unbounded support.