# Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)

arXiv: https://arxiv.org/abs/2509.22459 · HTML: https://mlsanity.com/paper/2509.22459/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 39 of its 48 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [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)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models](https://mlsanity.com/paper/2305.18455/) (2023)
- [Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation](https://mlsanity.com/paper/2404.04057/) (2024)
- [Diffusion-GAN: Training GANs with Diffusion](https://mlsanity.com/paper/2206.02262/) (2022)
- [Inductive Moment Matching](https://mlsanity.com/paper/2503.07565/) (2025)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [Let us Build Bridges: Understanding and Extending Diffusion Generative Models](https://mlsanity.com/paper/2208.14699/) (2022)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Non-Denoising Forward-Time Diffusions](https://mlsanity.com/paper/2312.14589/) (2023)
- [One-Step Diffusion Distillation via Deep Equilibrium Models](https://mlsanity.com/paper/2401.08639/) (2023)
- [Entropic Neural Optimal Transport via Diffusion Processes](https://mlsanity.com/paper/2211.01156/) (2022)

## Built on by (most cited first, 5 of 5)

- [IDLM: Inverse-distilled Diffusion Language Models](https://mlsanity.com/paper/2602.19066/) (2026)
- [Midpoint Generative Models](https://mlsanity.com/paper/2605.29920/) (2026)
- [Improved Distributional Diffusion Models](https://mlsanity.com/paper/2609.37147/) (2026)
- [Data Unlearning via Inverse Distillation](https://mlsanity.com/paper/2609.36099/) (2026)
- [One-Step Generation via Riemannian Wasserstein Gradient Flows](https://mlsanity.com/paper/2610.04454/) (2026)

## Abstract (arXiv)

While achieving exceptional generative quality, modern diffusion, flow, and other matching models suffer from slow inference, as they require many steps of iterative generation. Recent distillation methods address this problem by training efficient one-step generators under the guidance of a pre-trained teacher model. However, these methods are often constrained to only one specific framework, e.g., only to diffusion or only to flow models. Furthermore, these methods are originally data-free, and to benefit from the usage of real data, it is required to use an additional complex adversarial training with an extra discriminator model. In this paper, we present RealUID, a universal distillation framework for all matching models that seamlessly incorporates real data into the distillation procedure without GANs. Our RealUID approach offers a simple theoretical foundation that covers previous distillation methods for Flow Matching and Diffusion models, and can be also extended to their modifications, such as Bridge Matching and Stochastic Interpolants. The code can be found in https://github.com/David-cripto/RealUID.