Learning to Use Imagination: Progress-Conditioned Future Utilization for World Action Models

World Action Models (WAMs) extend Vision-Language-Action (VLA) models by incorporating future visual dynamics into action generation. However, existing WAMs often utilize imagined futures with limited adaptation to evolving execution progress, potentially introducing distracting or unreliable predictive cues. This limitation arises from two empirically identified forms of non-uniformity in future utility: (i) at the inter-progress level, the utility of imagined futures varies across execution stages as control demands change; and (ii) at the intra-progress level, individual future latents exhibit heterogeneous relevance within the same progress state. To address these limitations, we propose ProWAM, a Progress-Conditioned World Action Model that introduces execution progress as an explicit intermediate representation for adaptive imagination utilization. ProWAM comprises two tightly coupled components: (1) To obtain a reliable representation of execution progress, we propose the Self-Supervised Dual-Temporal Progress Encoder (SS-DTPE). SS-DTPE couples short-term action-observation interaction modeling with long-term recurrent progress aggregation to capture recent execution feedback and accumulated task history. (2) Conditioned on the progress representation from SS-DTPE, we propose the Hierarchical Progress-Conditioned Imagination Modulation (HPIM) to adapt imagination utilization to execution progress. HPIM operates at two complementary levels: an inter-progress global modulation mechanism adapts future utilization across execution stages, while an intra-progress relevance mechanism differentiates individual future latents within each progress state. Extensive experiments demonstrate consistent gains over strong VLA and WAM baselines.