  Can a pre-trained generator be adapted to the hybrid of multiple target
domains and generate images with integrated attributes of them? In this work,
we introduce a new task -- Few-shot Hybrid Domain Adaptation (HDA). Given a
source generator and several target domains, HDA aims to acquire an adapted
generator that preserves the integrated attributes of all target domains,
without overriding the source domain's characteristics. Compared with Domain
Adaptation (DA), HDA offers greater flexibility and versatility to adapt
generators to more composite and expansive domains. Simultaneously, HDA also
presents more challenges than DA as we have access only to images from
individual target domains and lack authentic images from the hybrid domain. To
address this issue, we introduce a discriminator-free framework that directly
encodes different domains' images into well-separable subspaces. To achieve
HDA, we propose a novel directional subspace loss comprised of a distance loss
and a direction loss. Concretely, the distance loss blends the attributes of
all target domains by reducing the distances from generated images to all
target subspaces. The direction loss preserves the characteristics from the
source domain by guiding the adaptation along the perpendicular to subspaces.
Experiments show that our method can obtain numerous domain-specific attributes
in a single adapted generator, which surpasses the baseline methods in semantic
similarity, image fidelity, and cross-domain consistency.
