Diffusion-based talking head generation has achieved remarkable visual quality, yet scaling it to long-term videos remains challenging. The widely adopted chunk-wise paradigm introduces two fundamental failures: (1) temporal-spatial misalignment between static identity references and dynamic audio streams, and (2) cascading identity drift propagated through self-generated continuity references across chunks. To address both issues, we propose AsymTalker, a novel diffusion-based talking head generation method comprising Temporal Reference Encoding (TRE) and Asymmetric Knowledge Distillation (AKD). First, TRE mitigates temporal-spatial misalignment by transforming the static identity image into a temporally coherent latent representation through encoding of a temporally replicated pseudo-video, without introducing additional parameters. Second, AKD resolves the inherent conditioning dilemma in chunk-wise training: using ground-truth references causes train-inference mismatch, while self-generated references entangle supervision with identity drift. Our asymmetric design circumvents this by anchoring the teacher model with ground-truth continuity references to provide drift-free, chunk-level supervision, thereby avoiding the teacher bottleneck. Meanwhile, the student model learns under inference-aligned conditions, conditioned only on self-generated references, and is trained via distribution matching to preserve identity over long horizons. Extensive experiments show AsymTalker achieves state-of-the-art results on HDTF and VFHQ. It guarantees high-fidelity, identity-consistent synthesis over 600-second videos and reaches a real-time inference speed of 66 FPS.