Abstract: Despite the success of diffusion models, thetraining and inference of diffusion models are notoriously expensive due to the long chain of the reverse process. In parallel, the Lottery Ticket Hypothesis (LTH) claims that there exists winning tickets (i.e., aproperly pruned sub-network together with original weight initialization) that canachieve performance competitive to the original dense neural network when trained in isolation. In this work, we for the first time apply LTH to diffusion models. We empirically find subnetworks at sparsity $90%-99%$ without compromisingperformance for denoising diffusion probabilistic models on benchmarks (CIFAR-10, CIFAR-100, MNIST). Moreover, existing LTH works identify the subnetworks with a unified sparsity along different layers. We observe that the similarity between two winning tickets of a model varies from block to block. Specifically, the upstream layers from two winning tickets for a model tend to be more similar than the downstream layers. Therefore, we propose to find the winning ticket with varying sparsity along different layers in the model. Experimentalresults demonstrate that our method can find sparser sub-models that require less memory for storageand reduce the necessary number of FLOPs. Codes are available at https://anonymous.4open.science/r/Lottery-Ticket-to-DDPM-2D79/.