Today's video-conferencing tools support a rich range of professional and social activities, but their generic, grid-based environments cannot be easily adapted to meet the varying needs of distributed collaborators. To enable end-user customization, we developed BlendScape, a system for meeting participants to compose video-conferencing environments tailored to their collaboration context by leveraging AI image generation techniques. BlendScape supports flexible representations of task spaces by blending users' physical or virtual backgrounds into unified environments and implements multimodal interaction techniques to steer the generation. Through an evaluation with 15 end-users, we investigated their customization preferences for work and social scenarios. Participants could rapidly express their design intentions with BlendScape and envisioned using the system to structure collaboration in future meetings, but experienced challenges with preventing distracting elements. We implement scenarios to demonstrate BlendScape's expressiveness in supporting distributed collaboration techniques from prior work and propose composition techniques to improve the quality of environments.