The Antarctic ice sheet is a major source of uncertainty in future sea-level projections, and physical simulators such as the PSU3D-ICE model are essential for studying its evolution. Calibrating them against observations is challenging: the simulator outputs and observed ice-thickness fields are high-dimensional, spatially dependent, and semi-continuous, with a large point mass at zero denoting ice-free regions. These features make conventional Gaussian-process emulation and likelihood-based calibration ill-suited and computationally infeasible at full resolution. We propose the sequential calibration method guided by a diffusion model and a Siamese network (SC-DS), a fully neural framework. For emulation, we develop a single conditional diffusion model that jointly generates the binary ice presence--absence pattern and the continuous thickness field, using global and local conditioning to represent how the input parameters shape the output. Because the emulator induces an intractable likelihood, our likelihood-free calibration replaces the hand-chosen distance and tolerance of approximate Bayesian computation with a probabilistic acceptance rule learned by an iteratively retrained Siamese network, together with a data--model discrepancy adjustment. Applied to the West Antarctic Ice Sheet, SC-DS matches the accuracy of state-of-the-art Gaussian-process calibration at a fraction of its computational cost and scales to the full-resolution domain, where existing methods become intractable.

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