Semantic map completion, which predicts the layout of unobserved regions from partial observations, is a critical capability for indoor robot navigation. Existing approaches either rely on high-dimensional discrete codebooks that inflate memory, or on iterative diffusion sampling that is too slow for real-time use. We present FastMap, a lightweight two-stage framework for completing top-down categorical semantic maps. First, a lookup-free BitVAE exploits the inherently binary (one-hot) structure of semantic maps to compress each map patch into compact bitwise tokens, yielding a 0.41GB model that is 3.7 times smaller than the prior masked-modeling baseline. Second, a Masked AutoEncoder (MAE)-style transformer reconstructs missing tokens in a single forward pass at 0.011s/map. To support object goal navigation, we additionally introduce an object-aware masking strategy that masks the target category during training and conditions generation on a learnable category embedding, without adding inference cost. On the Gibson benchmark, FastMap achieves 34.10% mIoU and 45.84% semantic Success Rate (sSR), more than doubling the previous best (21.88%), and reaches 83.8% Success Rate on downstream ObjectNav, the highest among the compared navigation methods.

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