# The Tractability Landscape of Sampling with Inexact Scores

arXiv: https://arxiv.org/abs/2607.19004 · HTML: https://mlsanity.com/paper/2607.19004/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 9 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [Convergence of the Inexact Langevin Algorithm in KL Divergence with Application to Score-based Generative Models](https://mlsanity.com/paper/2211.01512/) (2022)
- [On the Robustness of Langevin Dynamics to Score Function Error](https://mlsanity.com/paper/2603.11319/) (2026)

## Abstract (arXiv)

We provide a simple and tight characterization of the types of inexact score oracle access that permit sampling with vanishing total variation bias, for a standard, well-behaved target family. Our main result shows that any weaker error than the sub-Gaussian assumption used by [YW26] rules out the tractability of unbiased sampling. This strengthens the conclusion of [CCSW26] to be algorithm-agnostic, and to hold for a wider range of error assumptions.