Hyper-Diffusion is a novel approach that enables the estimation of both epistemic and aleatoric uncertainties using a single model. This method combines conditional denoising diffusion models with hyper-networks to efficiently estimate uncertainty without requiring an ensemble of models. The hyper-network generates a (pseudo-)ensemble of network weights for the diffusion model, allowing for accurate uncertainty estimation. The method is validated on two high-stakes tasks: x-ray computed tomography (CT) reconstruction and weather temperature forecasting. Aleatoric uncertainty, which arises from inherent variability in the task, is estimated by analyzing the variance of samples from the likelihood function. Epistemic uncertainty, reflecting the model's lack of knowledge, is estimated by analyzing the variance of samples from the posterior distribution. The hyper-diffusion model effectively captures both types of uncertainty by leveraging the properties of diffusion models and hyper-networks. The method is compared to existing approaches such as Monte Carlo dropout and deep ensembles. It demonstrates superior performance in estimating both aleatoric and epistemic uncertainties, particularly in scenarios with varying noise levels and dataset sizes. The results show that the hyper-diffusion model can accurately approximate the uncertainty estimates of a large ensemble with significantly reduced computational cost. In experiments on CT reconstruction and weather forecasting, the hyper-diffusion model outperforms other methods in terms of uncertainty estimation accuracy. It effectively isolates abnormal features in the data, providing reliable uncertainty maps. The model's ability to handle large-scale data and its efficiency in training make it a promising approach for uncertainty estimation in high-stakes applications. However, challenges remain in terms of computational efficiency and scalability, which are areas for future research.Hyper-Diffusion is a novel approach that enables the estimation of both epistemic and aleatoric uncertainties using a single model. This method combines conditional denoising diffusion models with hyper-networks to efficiently estimate uncertainty without requiring an ensemble of models. The hyper-network generates a (pseudo-)ensemble of network weights for the diffusion model, allowing for accurate uncertainty estimation. The method is validated on two high-stakes tasks: x-ray computed tomography (CT) reconstruction and weather temperature forecasting. Aleatoric uncertainty, which arises from inherent variability in the task, is estimated by analyzing the variance of samples from the likelihood function. Epistemic uncertainty, reflecting the model's lack of knowledge, is estimated by analyzing the variance of samples from the posterior distribution. The hyper-diffusion model effectively captures both types of uncertainty by leveraging the properties of diffusion models and hyper-networks. The method is compared to existing approaches such as Monte Carlo dropout and deep ensembles. It demonstrates superior performance in estimating both aleatoric and epistemic uncertainties, particularly in scenarios with varying noise levels and dataset sizes. The results show that the hyper-diffusion model can accurately approximate the uncertainty estimates of a large ensemble with significantly reduced computational cost. In experiments on CT reconstruction and weather forecasting, the hyper-diffusion model outperforms other methods in terms of uncertainty estimation accuracy. It effectively isolates abnormal features in the data, providing reliable uncertainty maps. The model's ability to handle large-scale data and its efficiency in training make it a promising approach for uncertainty estimation in high-stakes applications. However, challenges remain in terms of computational efficiency and scalability, which are areas for future research.