# Inductive Moment Matching

**Authors:** Linqi Zhou, Stefano Ermon, Jiaming Song  
**arXiv:** [2503.07565](https://arxiv.org/abs/2503.07565)  
**Date:** 2025-03-10  
**Summary page:** https://www.summarizepaper.com/en/paper/2503.07565v1/

## Key points

- Inductive Moment Matching (IMM) is a novel approach in generative models addressing trade-offs between sample generation quality and fast inference.
- IMM introduces a new class of generative models for one- or few-step sampling with single-stage training, avoiding instability and extensive tuning.
- IMM surpasses diffusion models on ImageNet-256x256 with an FID score of 1.99 using only 8 inference steps and achieves a state-of-the-art 2-step FID score of 1.98 on CIFAR-10 from scratch.
- The framework involves leveraging self-consistent interpolants to interpolate between data and prior distributions, matching all moments to improve convergence and outperform previous works while speeding up inference.
- IMPACT: Contributes to advancements in diffusion models, generative AI, democratizing content creation, expanding artistic expression, generating synthetic data for research purposes, but raises copyright concerns.

## Summary

Inductive Moment Matching (IMM) is a novel approach in the field of generative models that aims to address the trade-offs between high-quality sample generation and fast inference. Traditional diffusion models and Flow Matching techniques have been successful in generating high-quality samples but are slow during inference. However, distilling them into few-step models often leads to instability and requires extensive tuning. To overcome these challenges, IMM introduces a new class of generative models for one- or few-step sampling with a single-stage training procedure. Unlike distillation methods, IMM does not require pre-training initialization and optimization of two networks. Additionally, unlike Consistency Models, IMM guarantees distribution-level convergence and remains stable under various hyperparameters and standard model architectures. The results show that IMM surpasses diffusion models on ImageNet-256x256 with an FID score of 1.99 using only 8 inference steps. Furthermore, it achieves a state-of-the-art 2-step FID score of 1.98 on CIFAR-10 for a model trained from scratch. The framework of Inductive Moment Matching involves leveraging self-consistent interpolants to interpolate between data and prior distributions, followed by matching all moments of its own distribution to be closer to that of the data. This method ensures convergence in distribution and outperforms previous works across benchmarks while significantly speeding up the inference process. In terms of impact, this research contributes to advancements in diffusion models and generative AI and democratizing content creation. While there are potential benefits such as expanding artistic expression , and generating synthetic data for research purposes , copyright concerns . Overall, Inductive Moment Matching presents a promising new perspective on training few-step generative models from scratch and has the potential to inspire further developments in the field of generative modeling.