An ODE-based Sampler for Discrete Diffusion Models
Samson Gourevitch, Yazid Janati, Eric Moulines, Eric P. Xing, Alain Durmus, Giacomo Zanella
AI 速览：作者提出指数残差流（ERFs），为离散扩散模型构造类似概率流ODE的确定性采样框架，并证明其保持原扩散的边缘分布。
The marginals of a continuous diffusion model can be reproduced by a deterministic ordinary differential equation (ODE), known as the probability flow ODE, which provides a foundation for accelerated sampling and consistency distillation. In this paper we address the question whether an analogous formulation exists for discrete diffusion models and answer it affirmatively by introducing exponential residual flows (ERFs). Our framework augments the discrete state with a continuous residual variable for each token and position. These residuals evolve deterministically according to piecewise-defined ODEs whose vector fields depend on the current discrete state and the forward and backward rate matrices of the prescribed diffusion model. The discrete state changes whenever a residual reaches zero. We prove that this construction preserves the marginals of the original diffusion. We derive a practical discretization of our sampler and specialize it to masked and uniform diffusion. The deterministic trajectories of ERFs support consistency distillation and yield empirical improvements over previous approaches across a variety of benchmarks including code and text generation tasks.
Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation
Ilya Levin, Maksim Shuklin, Eric Moulines, Paul Mangold, Sergey Samsonov
AI 速览：该论文为联邦线性随机逼近建立Berry-Esseen型界与联邦高斯近似，并据此提出一种无需显式估计渐近协方差矩阵的在线乘子自助推断方法。
In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA). Our results provide the first federated Gaussian approximations for LSA that explicitly capture communication-computation trade-offs and heterogeneity-aware error terms, quantifying the effects of local step size, number of local updates, and heterogeneity on convergence rates. We present results for both (i) constant step size regime and (ii) decreasing step size with an increasing number of local iterations, recovering the recent rates of Bonnerjee et al. [2025] as a special case. As a primary application of our results, we develop an online multiplier bootstrap procedure for inference on the last iterate, which avoids explicit estimation of the asymptotic covariance matrix, and obtain non-asymptotic validity guarantees for this procedure.