Inductive Moment Matching

Linqi (Alex) Zhou, Stefano Ermon, Jiaming Song

International Conference on Machine Learning 2025 · Oral

In the rapidly evolving landscape of generative AI, particularly in visual domains, **diffusion models** and **flow matching** have emerged as dominant paradigms, powering sophisticated text-to-image and text-to-video systems. While these models have achieved unprecedented levels of realism, they frequently grapple with a fundamental challenge often termed the "generative trilemma": the difficulty in simultaneously achieving high sample quality, stable training, and efficient inference. This talk introduces **Inductive Moment Matching (IMM)**, a novel approach designed to address this trilemma head-on, offering a single-stage training objective that promises to deliver all three desirable properties.

AI review

IMM is a competent and well-motivated contribution to the generative modeling literature. It combines two ideas — injecting the target timestep into the network to overcome DDIM's linearity, and using an inductive MMD objective to stabilize training — into a single-stage framework that achieves respectable FID numbers at low step counts. The empirical results are credible and the motivation is clear. What holds this back from a higher rating is that neither component is technically novel in isolation: MMD-based generative objectives predate this work substantially, consistency models already…