# Bootstrapping Diffusion: Diffusion Model Training Leveraging Partial and Corrupted Data

arXiv: https://arxiv.org/abs/2505.11825 · HTML: https://mlsanity.com/paper/2505.11825/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 17 May 2025.

## Placed in

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

## Builds on (most cited first, 20 of 20)

- [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)
- [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)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2212.04493/) (2022)
- [Versatile Diffusion: Text, Images and Variations All in One Diffusion Model](https://mlsanity.com/paper/2211.08332/) (2022)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Data](https://mlsanity.com/paper/2404.10177/) (2024)
- [Scaling Laws For Diffusion Transformers](https://mlsanity.com/paper/2410.08184/) (2024)
- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [An Expectation-Maximization Algorithm for Training Clean Diffusion Models from Corrupted Observations](https://mlsanity.com/paper/2407.01014/) (2024)
- [On Measuring Excess Capacity in Neural Networks](https://mlsanity.com/paper/2202.08070/) (2022)

## Abstract (arXiv)

Training diffusion models requires large datasets. However, acquiring large volumes of high-quality data can be challenging, for example, collecting large numbers of high-resolution images and long videos. On the other hand, there are many complementary data that are usually considered corrupted or partial, such as low-resolution images and short videos. Other examples of corrupted data include videos that contain subtitles, watermarks, and logos. In this study, we investigate the theoretical problem of whether the above partial data can be utilized to train conventional diffusion models. Motivated by our theoretical analysis in this study, we propose a straightforward approach of training diffusion models utilizing partial data views, where we consider each form of complementary data as a view of conventional data. Our proposed approach first trains one separate diffusion model for each individual view, and then trains a model for predicting the residual score function. We prove generalization error bounds, which show that the proposed diffusion model training approach can achieve lower generalization errors if proper regularizations are adopted in the residual score function training. In particular, we prove that the difficulty in training the residual score function scales proportionally with the signal correlations not captured by partial data views. Consequently, the proposed approach achieves near first-order optimal data efficiency.