Abstract: Diffusion models (DMs) have shown remarkable capabilities in generating realistic high-quality images, audios, and videos. They benefit significantly from extensive pre-training on large-scale datasets, including web-crawled data with paired data and conditions, such as image-text and image-class pairs.Despite rigorous filtering, these pre-training datasets often inevitably contain corrupted pairs where conditions do not accurately describe the data. This paper presents the first comprehensive study on the impact of such corruption in pre-training data of DMs.We synthetically corrupt ImageNet-1K and CC3M to pre-train and evaluate over $50$ conditional DMs. Our empirical findings reveal that various types of slight corruption in pre-training can significantly enhance the quality, diversity, and fidelity of the generated images across different DMs, both during pre-training and downstream adaptation stages. Theoretically, we consider a Gaussian mixture model and prove that slight corruption in the condition leads to higher entropy and a reduced 2-Wasserstein distance to the ground truth of the data distribution generated by the corruptly trained DMs.Inspired by our analysis, we propose a simple method to improve the training of DMs on practical datasets by adding condition embedding perturbations (CEP).CEP significantly improves the performance of various DMs in both pre-training and downstream tasks.We hope that our study provides new insights into understanding the data and pre-training processes of DMs.