# The Emergence of Reproducibility and Generalizability in Diffusion Models

arXiv: https://arxiv.org/abs/2310.05264 · HTML: https://mlsanity.com/paper/2310.05264/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 62 of its 83 references that are in the map.
- First posted on arXiv 8 Oct 2023.

## Placed in

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

## Builds on (most cited first, 30 of 62)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [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)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [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)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [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)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [All are Worth Words: A ViT Backbone for Diffusion Models](https://mlsanity.com/paper/2209.12152/) (2022)

## Built on by (most cited first, 21 of 21)

- [The Unreasonable Effectiveness of Gaussian Score Approximation for Diffusion Models and its Applications](https://mlsanity.com/paper/2412.09726/) (2024)
- [Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models](https://mlsanity.com/paper/2505.16959/) (2025)
- [On the Edge of Memorization in Diffusion Models](https://mlsanity.com/paper/2508.17689/) (2025)
- [Unleashing the Potential of Diffusion Models for End-to-End Autonomous Driving](https://mlsanity.com/paper/2602.22801/) (2026)
- [Resolving Memorization in Empirical Diffusion Model for Manifold Data in High-Dimensional Spaces](https://mlsanity.com/paper/2505.02508/) (2025)
- [From Navigation to Refinement: Revealing the Two-Stage Nature of Flow-based Diffusion Models through Oracle Velocity](https://mlsanity.com/paper/2512.02826/) (2025)
- [VCISR: Blind Single Image Super-Resolution with Video Compression Synthetic Data](https://mlsanity.com/paper/2311.00996/) (2023)
- [The Generation Phases of Flow Matching: a Denoising Perspective](https://mlsanity.com/paper/2510.24830/) (2025)
- [A Random Matrix Theory Perspective on the Consistency of Diffusion Models](https://mlsanity.com/paper/2602.02908/) (2026)
- [TimeAutoDiff: A Unified Framework for Generation, Imputation, Forecasting, and Time-Varying Metadata Conditioning of Heterogeneous Time Series Tabular Data](https://mlsanity.com/paper/2406.16028/) (2024)
- [UniRes: Universal Image Restoration for Complex Degradations](https://mlsanity.com/paper/2506.05599/) (2025)
- [Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold](https://mlsanity.com/paper/2602.06021/) (2026)
- [When and how can inexact generative models still sample from the data manifold?](https://mlsanity.com/paper/2508.07581/) (2025)
- [Flow Matching in the Low-Noise Regime: Pathologies and a Contrastive Remedy](https://mlsanity.com/paper/2509.20952/) (2025)
- [A solvable generative model with a linear, one-step denoiser](https://mlsanity.com/paper/2411.17807/) (2024)
- [Diagonally-Weighted Generalized Method of Moments Estimation for Gaussian Mixture Modeling](https://mlsanity.com/paper/2507.20459/) (2025)
- [Generation Properties of Stochastic Interpolation under Finite Training Set](https://mlsanity.com/paper/2509.21925/) (2025)
- [Latent Iterative Refinement Flow: A Geometric Constrained Approach for Few-Shot Generation](https://mlsanity.com/paper/2509.19903/) (2025)
- [Point-to-Point: Sparse Motion Guidance for Controllable Video Editing](https://mlsanity.com/paper/2511.18277/) (2025)
- [Transformer-based Diffusion models for Hydrological Time Series Probabilistic Imputation and Forecasting](https://mlsanity.com/paper/2607.21200/) (2026)
- [Memorization and Malign Generalization in Conditional Diffusion Models with Random Features](https://mlsanity.com/paper/2610.11288/) (2026)

## Abstract (arXiv)

In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often yield remarkably similar outputs. We confirm this phenomenon through comprehensive experiments, implying that different diffusion models consistently reach the same data distribution and scoring function regardless of diffusion model frameworks, model architectures, or training procedures. More strikingly, our further investigation implies that diffusion models are learning distinct distributions affected by the training data size. This is supported by the fact that the model reproducibility manifests in two distinct training regimes: (i) "memorization regime", where the diffusion model overfits to the training data distribution, and (ii) "generalization regime", where the model learns the underlying data distribution. Our study also finds that this valuable property generalizes to many variants of diffusion models, including those for conditional use, solving inverse problems, and model fine-tuning. Finally, our work raises numerous intriguing theoretical questions for future investigation and highlights practical implications regarding training efficiency, model privacy, and the controlled generation of diffusion models.