Theoretical analysis proves that Langevin dynamics is fundamentally non-robust to score function errors, justifying the shift to Diffusion Models.
March 13, 2026
Original Paper
On the Robustness of Langevin Dynamics to Score Function Error
arXiv · 2603.11319
The Takeaway
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