This paper investigates the phenomenon of hallucinations in diffusion models, identifying a new failure mode called "mode interpolation." Hallucinations occur when diffusion models generate samples that lie completely outside the support of the training distribution. The authors show that diffusion models interpolate between nearby data modes in the training set, generating samples that do not exist in the original data. This leads to the creation of artifacts that never existed in real data, i.e., hallucinations. The paper explores this phenomenon through experiments on 1D and 2D Gaussian datasets, showing how a discontinuous loss landscape in the diffusion model's decoder leads to hallucinations. It also demonstrates how hallucination leads to the generation of combinations of shapes that never existed in the training data. The authors extend this understanding to real-world datasets, explaining the unexpected generation of images with additional or missing fingers similar to those produced by popular text-to-image generative models. The paper also shows that diffusion models know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling steps. Using a simple metric to capture this variance, the authors can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples in the synthetic datasets. The paper concludes by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and a 2D Gaussian dataset. The authors release their code at https://github.com/locuslab/diffusion-model-hallucination.This paper investigates the phenomenon of hallucinations in diffusion models, identifying a new failure mode called "mode interpolation." Hallucinations occur when diffusion models generate samples that lie completely outside the support of the training distribution. The authors show that diffusion models interpolate between nearby data modes in the training set, generating samples that do not exist in the original data. This leads to the creation of artifacts that never existed in real data, i.e., hallucinations. The paper explores this phenomenon through experiments on 1D and 2D Gaussian datasets, showing how a discontinuous loss landscape in the diffusion model's decoder leads to hallucinations. It also demonstrates how hallucination leads to the generation of combinations of shapes that never existed in the training data. The authors extend this understanding to real-world datasets, explaining the unexpected generation of images with additional or missing fingers similar to those produced by popular text-to-image generative models. The paper also shows that diffusion models know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling steps. Using a simple metric to capture this variance, the authors can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples in the synthetic datasets. The paper concludes by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and a 2D Gaussian dataset. The authors release their code at https://github.com/locuslab/diffusion-model-hallucination.