Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions.

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood.

In this regard, the design of stronger adversarial attacks plays a crucial role in understanding the nature of possible real-world threats.

Recent years have seen increasing use of supervised learning methods for segmentation tasks. However, the predictive performance of these algorithms depends on the quality of labels.

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.

Our contributions can be summarized as follows.