Recent text-to-image diffusion models have significantly improved visual quality and text alignment. However, generating a sequence of images while preserving consistent character identity across diverse scenes remains challenging. Existing methods often face a trade-off between maintaining identity consistency and per-image prompt alignment. In this paper, we introduce AsemConsist, a framework that resolves this trade-off through selective text embedding modification, enabling consistent identity preservation without degrading per-image prompt alignment. We further analyze the semantic structure of padding embeddings and find that, in multi-encoder backbones, only padding embeddings that retain prompt-related semantics can effectively serve as semantic containers. Based on this observation, we selectively inject per-image semantics into such padding embeddings while suppressing prompt-irrelevant components. Additionally, we propose an adaptive feature-sharing strategy that automatically evaluates identity specificity and selectively applies constraints only to ambiguous identity prompts. Finally, we propose a unified evaluation metric called SeeSaw, which measures the balance between identity consistency and per-image alignment while evaluating whether identity and per-image prompts are equally reflected in generated images. Our method demonstrates superior performance over existing competitors when built upon SD3.5 and FLUX backbones, highlighting its effectiveness across different architectures and text encoders. Project page: https://minjung-s.github.io/asemconsist

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