We argue that diffusion models' success in modeling complex distributions is, for the most part, coming from their conditioning. This paper investigates the representation used to condition diffusion models from the perspective that ideal representations should improve modeling the data distribution, be easy to generate, and be compositional to allow generalizing outside the training distribution. We introduce Discrete Latent Code (DLC), an image representation derived from Simplicial Embeddings trained with a self-supervised learning objective. DLCs are sequences of discrete tokens, as opposed to the standard continuous image embeddings. They are easy to generate and their compositionality enables sampling of novel images beyond the training distribution. Diffusion models trained with DLCs improve generation fidelity, establishing a new state-of-the-art for unconditional image generation on ImageNet. Additionally, we show that composing DLCs allows the image generator to produce interesting out-of-distribution samples that coherently combine the semantics of images in diverse ways. Finally, we showcase how DLCs can enable text-to-image generation by leveraging large-scale pretrained language models. Using only 9M image-caption pairs, we efficiently finetune a text diffusion model to generate novel DLCs that produces samples outside of the data distribution used to train the image generator.

Maximizing the area under the receiver operating characteristic curve (AUC) is a popular approach to imbalanced binary classification problems. Existing AUC maximization methods usually assume that training and test distributions are identical. However, this assumption is often violated in practice due to {\it a positive distribution shift}, where the negative-conditional density does not change but the positive-conditional density can vary. This shift often occurs in imbalanced classification since positive data are often more diverse and time-varying than negative data. To deal with this shift, we theoretically show that the AUC on the test distribution can be expressed by using the positive and marginal training densities and the marginal test density. Based on this result, we can maximize the AUC on the test distribution by using positive and unlabeled data in the training distribution and unlabeled data in the test distribution. The proposed method requires only positive labels in the training distribution as supervision. Moreover, the derived AUC has a simple form and thus is easy to implement. The effectiveness of the proposed method is shown with four real-world datasets.

"Effective robustness" measures the extra out-of-distribution (OOD) robustness

However, sampling is not the only source of uncertainty. In practice, distributions change between locations and across time.

In safety-critical applications, machine learning models should generalize well under worst-case distribution shifts, that is, have a small robust risk.

One of the primary drivers of the success of machine learning methods in open-world perception settings, such ascomputer vision [19]and NLP [8],has been the ability ofhigh-capacity function approximators, suchasdeepneuralnetworks,tolearngeneralizable modelsfromlargeamountsof data.

Thisresult shows that visual grounding/feature attribution can be ineffective at resolving shortcuts.