Overall, properly representing aleatoric uncertainty is a challenging but fundamentally important consideration in Bayesian classification. We have shown that posterior tempering provides a mechanism to more honestly represent our beliefs about aleatoric uncertainty, especially in the presence of data augmentation. In general, as in Wilson and Izmailov [ 62 ], we should not be alarmed if T =1 is not optimal in sophisticated models on complex real-world datasets. Moreover, we have shown how other mechanisms to represent aleatoric uncertainty, such as the noisy Dirichlet model, 17 do not suffer from a cold posterior effect in the presence of data augmentation. Indeed, while an interesting phenomenon, cold posteriors should not be conflated with the success or failure of Bayesian deep learning.

Although there have been many remarkable advances in recent years, one of the most critical problems in this direction has been that previous methods work only with simple and synthetic scenes but not with complex and naturalistic images or videos.

We present an approach for lifelong/continual learning of convolutional neural networks (CNN) that does not suffer from the problem of catastrophic forgetting when moving from one task to the other. We show that the activation maps generated by the CNN trained on the old task can be calibrated using very few calibration parameters, to become relevant to the new task.

These previous methods mainly focus on unconditional generative modeling. While there exist guided-diffusion models (Song and Ermon, 2019; Song et al., 2021c; Dhariwal and Nichol, 2021; Nichol et al., 2022; Ramesh et al., 2022) that target on generating high-resolution photo-realistic images that match the semantic meanings or content of the label, text, or corrupted-images, we focus on studying diffusion-based conditional generative modeling at a more fundamental level.