Comparison with Sample-wise AT. Previous works (Hendrycks et al. 2021;Yi et al. 2021) try to exploit samplewise AT as a **data** augmentation strategy to obtain higher OOD performance. However, the performance only improves when the distribution shift is dominated by diversity shift, e.g., noise, and blurring. Otherwise, performance might be degraded, as shown in Table 1. One possible explanation is that sample-wise AT fails to capture the domain-level variations as DAT. As a result, it may add perturbations to the invariant features and hurt performance, especially under correlation shift.