Cross-modal medical image synthesis research focuses on reconstructing missing imaging modalities from available ones to support clinical diagnosis. Driven by clinical necessities for flexible modality reconstruction, we explore K to N medical generation, where three critical challenges emerge: How can we model the heterogeneous contributions of different modalities to various target tasks? How can we ensure fusion quality control to prevent degradation from noisy information? How can we maintain modality identity consistency in multi-output generation? Driven by these clinical necessities, and drawing inspiration from SAM2's sequential frame paradigm and clinicians' progressive workflow of incrementally adding and selectively integrating multi-modal information, we treat multi-modal medical data as sequential frames with quality-driven selection mechanisms. Our key idea is to "learn" adaptive weights for each modality-task pair and "memorize" beneficial fusion patterns through progressive enhancement. To achieve this, we design three collaborative modules: PreWeightNet for global contribution assessment, ThresholdNet for adaptive filtering, and EffiWeightNet for effective weight computation. Meanwhile, to maintain modality identity consistency, we propose the Causal Modality Identity Module (CMIM) that establishes causal constraints between generated images and target modality descriptions using vision-language modeling. Extensive experimental results demonstrate that our proposed Med-K2N outperforms state-of-the-art methods by significant margins on multiple benchmarks. Source code is available.