Research to date in AI and dementia has primarily focused on medical and care-giver applications. This study complements prior work by collecting qualitative data from individuals with Mild Cognitive Impairment (MCI), and mild-to-moderate dementia, uncovering their perspectives, envisioned use cases, and anticipated challenges with generative AI applications. Findings uncover ways people with MCI and dementia want to use AI to engage in resilience building activities related to fostering wellness, building social connections, and finding purpose. However, each of these use cases came with tradeoffs in embracing healthy thinking. Based on these findings, we discuss directions for future work in AI for resilience building in dementia. We intend for this work to lay the groundwork for future research in AI design and development to empower people living with dementia to engage in resilience building activities, which may have lasting positive impacts on their mental health and well-being.