# Inductive Moment Matching

arXiv: https://arxiv.org/abs/2503.07565 · HTML: https://mlsanity.com/paper/2503.07565/

## Key facts

- Cited by 113 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 64 of its 69 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 64)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)

## Built on by (most cited first, 30 of 113)

- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Improved Mean Flows: On the Challenges of Fastforward Generative Models](https://mlsanity.com/paper/2512.02012/) (2025)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Diffuse and Disperse: Image Generation with Representation Regularization](https://mlsanity.com/paper/2506.09027/) (2025)
- [One-step Latent-free Image Generation with Pixel Mean Flows](https://mlsanity.com/paper/2601.22158/) (2026)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [AlphaFlow: Understanding and Improving MeanFlow Models](https://mlsanity.com/paper/2510.20771/) (2025)
- [Representation Fr'echet Loss for Visual Generation](https://mlsanity.com/paper/2604.28190/) (2026)
- [Transition Models: Rethinking the Generative Learning Objective](https://mlsanity.com/paper/2509.04394/) (2025)
- [pi-Flow: Policy-Based Few-Step Generation via Imitation Distillation](https://mlsanity.com/paper/2510.14974/) (2025)
- [There is No VAE: End-to-End Pixel-Space Generative Modeling via Self-Supervised Pre-training](https://mlsanity.com/paper/2510.12586/) (2025)
- [One-Step Generative Modeling via Wasserstein Gradient Flows](https://mlsanity.com/paper/2605.11755/) (2026)
- [Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling](https://mlsanity.com/paper/2510.24474/) (2025)
- [Terminal Velocity Matching](https://mlsanity.com/paper/2511.19797/) (2025)
- [CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Models](https://mlsanity.com/paper/2509.24526/) (2025)
- [Joint Distillation for Fast Likelihood Evaluation and Sampling in Flow-based Models](https://mlsanity.com/paper/2512.02636/) (2025)
- [Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences](https://mlsanity.com/paper/2603.10592/) (2026)
- [Simulating the Visual World with Artificial Intelligence: A Roadmap](https://mlsanity.com/paper/2511.08585/) (2025)
- [Learn to Guide Your Diffusion Model](https://mlsanity.com/paper/2510.00815/) (2025)
- [Flow Map Distillation Without Data](https://mlsanity.com/paper/2511.19428/) (2025)
- [Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instruction](https://mlsanity.com/paper/2505.20755/) (2025)
- [Learning an Image Editing Model without Image Editing Pairs](https://mlsanity.com/paper/2510.14978/) (2025)
- [SoFlow: Solution Flow Models for One-Step Generative Modeling](https://mlsanity.com/paper/2512.15657/) (2025)
- [Adversarial Flow Models](https://mlsanity.com/paper/2511.22475/) (2025)
- [Stable Velocity: A Variance Perspective on Flow Matching](https://mlsanity.com/paper/2602.05435/) (2026)
- [Scale-wise Distillation of Diffusion Models](https://mlsanity.com/paper/2503.16397/) (2025)
- [One-Step Flow Q-Learning: Addressing the Diffusion Policy Bottleneck in Offline Reinforcement Learning](https://mlsanity.com/paper/2508.13904/) (2025)
- [On the Wasserstein Gradient Flow Interpretation of Drifting Models](https://mlsanity.com/paper/2605.05118/) (2026)

## Abstract (arXiv)

Diffusion models and Flow Matching generate high-quality samples but are slow at inference, and distilling them into few-step models often leads to instability and extensive tuning. To resolve these trade-offs, we propose Inductive Moment Matching (IMM), a new class of generative models for one- or few-step sampling with a single-stage training procedure. Unlike distillation, IMM does not require pre-training initialization and optimization of two networks; and unlike Consistency Models, IMM guarantees distribution-level convergence and remains stable under various hyperparameters and standard model architectures. IMM surpasses diffusion models on ImageNet-256x256 with 1.99 FID using only 8 inference steps and achieves state-of-the-art 2-step FID of 1.98 on CIFAR-10 for a model trained from scratch.