On the Robustness of Langevin Dynamics to Score Function Error
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
We consider the robustness of score-based generative modeling to errors in the estimate of the score function. In particular, we show that Langevin dynamics is not robust to the L2 errors (more generally Lp errors) in the estimate of the score function. It is well-established that with small L2 errors in the estimate of the score function, diffusion models can sample faithfully from the target distribution under fairly mild regularity assumptions in a polynomial time horizon. In contrast, our work shows that even for simple distributions in high dimensions, Langevin dynamics run for any polynomial time horizon will produce a distribution far from the target distribution in Total Variation (TV) distance, even when the L2 error (more generally Lp) of the estimate of the score function is arbitrarily small. Considering such an error in the estimate of the score function is unavoidable in practice when learning the score function from data, our results provide further justification for diffusion models over Langevin dynamics and serve to caution against the use of Langevin dynamics with estimated scores.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 41 of its 70 references that are in the map. First posted on arXiv 11 Mar 2026.
Builds on
41 of 70 references.
Closest ancestors · 15
Same direction, newest first
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- 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
3 more
Other references · 26
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- 2019Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Modelcited by 147
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- 2024Optimization, Isoperimetric Inequalities, and Sampling via Lyapunov Potentialscited by 1
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Citing papers per year: 2026: 2.
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