Understanding and modeling human mobility is central to challenges in transport planning, sustainable urban design, and public health. Despite decades of effort, simulating individual mobility remains challenging because of its complex, context-dependent, and exploratory nature. Here, building on the activity-based view of daily mobility, we propose MobilityGen, a diffusion-based generative framework for simulating multi-attribute activity-travel sequences over days to weeks at large spatial scales. By linking behavioral attributes with environmental context, MobilityGen reproduces key patterns such as scaling laws for location visits, activity time allocation, and the coupled evolution of travel mode and destination choices. It reflects spatio-temporal variability and generates diverse and plausible mobility patterns consistent with the built environment. Beyond standard validation, MobilityGen enables analyses that have been difficult with earlier models, including how access to urban space varies across travel modes and how co-presence dynamics shape social exposure and segregation. Together, these results support an integrated, data-driven basis for fine-grained studies of human mobility behavior and its societal implications.