SLAI Seminar 27th Session will be discussing the topic on "Mathematical foundations of generative diffusion models",  from 2:30pm to 4pm, March 5th (Thursday) at Room B401, online participation is welcome 

(Tencent Meeting ID: 946-581-613)

报告主题：生成扩散模型的数学基础

时间：2026年3月5日（周四）下午14:30-16:00

地点: 深圳河套学院B401教室

线上参与：腾讯会议号946-581-613

主讲嘉宾：Nikita Puchkin教授

主持人：陈淙靓教授

讲者简介 About the Speaker:

Nikita Puchkin教授分别于2016年和2018年获莫斯科物理技术学院应用数学与物理学专业学士学位与硕士学位（荣誉学位），2018年同时获斯科尔科沃科技学院数学与计算机科学专业硕士学位（荣誉学位）。2023年在俄罗斯高等经济大学取得数学博士学位，师从V. Spokoiny教授。Puchkin教授曾荣获2020年度俄罗斯青年数学家奖、2024年度青年领军学者基金（数学领域）。自2024年9月，他担任俄罗斯高等经济大学人工智能模型理论基础实验室主任。

N. Puchkin received his B.Sc. and M.Sc. (Hons.) degrees in applied mathematics and physics from the Moscow Institute of Physics and Technology in 2016 and 2018, respectively, and an additional M.Sc. (Hons.) degree in mathematics and computer science from the Skolkovo Institute of Science and Technology in 2018. In 2023, he obtained a Ph.D. in mathematics from HSE University under the supervision of Prof. Dr. V. Spokoiny. He was awarded the 2020 Young Russian Mathematics Award and the 2024 Junior Leader Grant (mathematics). Since September 2024, he has been leading the Laboratory for Theoretical Foundations of AI Models at HSE University.

报告摘要：

生成扩散模型已成为基于非平衡热力学的数据合成领域的重要范式，不仅推动我们向高质量图像生成迈出关键一步，更催生了流匹配、扩散薛定谔桥等前沿新兴方法。本次报告将系统阐述去噪扩散概率模型与基于分数的生成模型的数学基础，重点剖析估计与推断两个核心阶段。我们将着重比较基于随机微分方程与常微分方程的采样方案，并深入探讨分数估计的复杂度问题。

Abstract: 

Generative diffusion models have emerged as a powerful paradigm for data synthesis based on non‑equilibrium thermodynamics. They have allowed us to take a significant step towards generating high‑quality images and have also given rise to state‑of‑the‑art and emerging methods, such as flow matching and diffusion Schrödinger bridges. In my talk, I will discuss the mathematical foundations of denoising diffusion probabilistic models (DDPM) and score‑based generative models, with particular attention to both the estimation and inference phases. The main focus will be on comparing SDE‑ and ODE‑based sampling schemes and on the complexity of score estimation.