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Conversational image generation requires a model to follow user instructions across multiple rounds of interaction, grounded in interleaved text and images that accumulate as chat history. While recent multimodal large language models (MLLMs) can generate and edit images, most existing multi-turn benchmarks and training recipes are effectively Markov: the next output depends primarily on the most recent image, enabling shortcut solutions that ignore long-range history. In this work we formalize and target the more challenging non-Markov setting, where a user may refer back to earlier states, undo changes, or reference entities introduced several rounds ago. We present (i) non-Markov multi-round data construction strategies, including rollback-style editing that forces retrieval of earlier visual states and name-based multi-round personalization that binds names to appearances across rounds; (ii) a history-conditioned training and inference framework with token-level caching to prevent multi-round identity drift; and (iii) enabling improvements for high-fidelity image reconstruction and editable personalization, including a reconstruction-based DiT detokenizer and a multi-stage fine-tuning curriculum. We demonstrate that explicitly training for non-Markov interactions yields substantial improvements in multi-round consistency and instruction compliance, while maintaining strong single-round editing and personalization.