publications

2025

1. conference

   Variational Inference on the Boolean Hypercube with the Quantum Entropy

   Eliot Beyler, and Francis Bach

   In International Conference on Artificial Intelligence and Statistics (AISTATS), 2025

   Abs arXiv Bib PDF Code

   In this paper, we derive variational inference upper-bounds on the log-partition function of a pairwize Markov random fields on the Boolean hypercube, based on quantum relaxations of the Kullback-Leibler divergence. We then propose an efficient algorithm to compute these bounds based on primal-dual optimization. An improvement of these bounds through the use of "hierarchies", similar to sum-of-squares (SoS) hierarchies is proposed, and we present a greedy algorithm to select among these relaxations. We carry extensive numerical experiments and compare with state-of-the-art methods for this inference problem.

   @inproceedings{beylerVariationalInferenceBoolean2025,
     title = {Variational {{Inference}} on the {{Boolean Hypercube}} with the {{Quantum Entropy}}},
     booktitle = {International {{Conference}} on {{Artificial Intelligence}} and {{Statistics}} ({{AISTATS}})},
     author = {Beyler, Eliot and Bach, Francis},
     year = {2025},
   }

2. journal

   Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity

   Eliot Beyler, and Francis Bach

   Journal of Machine Learning Research, 2025

   Abs arXiv Bib PDF

   Score-based generative models achieve state-of-the-art sampling performance by denoising a distribution perturbed by Gaussian noise. In this paper, we focus on a single deterministic denoising step, and compare the optimal denoiser for the quadratic loss, we name "full-denoising", to the alternative "half-denoising" introduced by Hyvärinen (2025). We show that looking at the performance in terms of distance between distributions tells a more nuanced story, with different assumptions on the data leading to very different conclusions. We prove that half-denoising is better than full-denoising for regular enough densities, while full-denoising is better for singular densities such as mixtures of Dirac measures or densities supported on a low-dimensional subspace. In the latter case, we prove that full-denoising can alleviate the curse of dimensionality under a linear manifold hypothesis.

   @article{beylerOptimalDenoisingScoreBased2025,
     title = {Optimal {{Denoising}} in {{Score-Based Generative Models}}: {{The Role}} of {{Data Regularity}}},
     author = {Beyler, Eliot and Bach, Francis},
     year = {2025},
     journal = {Journal of Machine Learning Research},
     volume = {26},
     number = {293},
     pages = {1--48},
   }

3. preprint

   Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance

   Eliot Beyler, and Francis Bach

   2025

   Abs arXiv Bib

   We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze discretization, initialization, and score estimation errors. Notably, we derive the first Wasserstein convergence bound for the Heun sampler and improve existing results for the Euler sampler of the probability flow ODE. Our analysis emphasizes the importance of spatial regularity of the learned score function and argues for controlling the score error with respect to the true reverse process, in line with denoising score matching. We also incorporate recent results on smoothed Wasserstein distances to sharpen initialization error bounds.

   @article{beylerConvergenceDeterministicStochastic2025,
     title = {Convergence of {{Deterministic}} and {{Stochastic Diffusion-Model Samplers}}: {{A Simple Analysis}} in {{Wasserstein Distance}}},
     shorttitle = {Convergence of {{Deterministic}} and {{Stochastic Diffusion-Model Samplers}}},
     author = {Beyler, Eliot and Bach, Francis},
     year = {2025},
   }