Recent advancements in generative artificial intelligence (AI) have disrupted assessment practices within the higher education sector. The efficacy of existing assessment approaches is under reexamination with the introduction of generative AI's ability to generate human-like text. Simultaneously, there are calls to integrate generative AI into assessment design to enhance learning and prepare students for a new era of technology in their careers. This paper proposes a framework to integrate generative AI into formative and summative assessments across Bloom's levels and Knowledge Dimensions. Its purpose is to illustrate the versatility and intricacy of generative AI's potential applications grounded in existing learning theory while retaining a focus on authentic assessment. The goal is to support higher education professionals stimulate assessment design concepts featuring generative AI positioned within varying learning complexities.