  We tackle the domain generalisation (DG) problem by posing it as a domain
adaptation (DA) task where we adversarially synthesise the worst-case target
domain and adapt a model to that worst-case domain, thereby improving the
model's robustness. To synthesise data that is challenging yet
semantics-preserving, we generate Fourier amplitude images and combine them
with source domain phase images, exploiting the widely believed conjecture from
signal processing that amplitude spectra mainly determines image style, while
phase data mainly captures image semantics. To synthesise a worst-case domain
for adaptation, we train the classifier and the amplitude generator
adversarially. Specifically, we exploit the maximum classifier discrepancy
(MCD) principle from DA that relates the target domain performance to the
discrepancy of classifiers in the model hypothesis space. By Bayesian
hypothesis modeling, we express the model hypothesis space effectively as a
posterior distribution over classifiers given the source domains, making
adversarial MCD minimisation feasible. On the DomainBed benchmark including the
large-scale DomainNet dataset, the proposed approach yields significantly
improved domain generalisation performance over the state-of-the-art.
