Abstract. Target speaker extraction (TSE) isolates a desired speaker from a multi-speaker mixture using cues that identify the target. Prior work has explored acoustic and textual cues, such as enrollment audio and different types of speaker descriptors, but typically relies on a single cue family. Yet no single cue is both broadly available and reliably discriminative. Moreover, most TSE systems adopt mask-prediction models, which are prone to audible artifacts and generalize poorly across acoustic conditions. To address these limitations, we propose PromptSep-Speaker, a generative TSE model based on latent diffusion that unifies four interchangeable cues: speaker temporal order, transcript, enrollment audio, and speaker caption. The generative formulation delivers higher separation quality and multimodal prompting improves applicability across scenarios. To fully exploit each cue, we further introduce a frozen WavLM representation with an auxiliary alignment loss that supervises query-mixture cross-attention without extra labeling. Across four evaluation sets and a listening study, PromptSep-Speaker achieves state-of-the-art performance over TSE and universal source separation baselines, improving separation accuracy and quality across cue modalities.