Theoretical analysis proves that Langevin dynamics is fundamentally non-robust to score function errors, justifying the shift to Diffusion Models.
arXiv · March 13, 2026 · 2603.11319
Why it matters
While practitioners have largely moved to diffusion, this paper provides the mathematical proof that Langevin dynamics fail in high dimensions even with small score errors. This provides a rigorous foundation for why diffusion's time-dependent score estimation is necessary.
From the abstract
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 L^2 errors (more generally L^p errors) in the estimate of the score function. It is well-established that with small L^2 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