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Often originating from unconverged or inconsistent electronic-structure calculations, this noise is challenging to identify. Existing mitigation strategies, such as manual filtering or iterative refinement of outliers, require either substantial expert effort or multiple expensive retraining cycles, making them difficult to scale to large datasets. Here, we introduce a noise-resilient training method that automatically down-weighs noisy samples, without requiring additional reference calculations. By tracking the loss distribution via an exponential moving average, this unsupervised method identifies outliers throughout a single training run. We show that this approach prevents overfitting and matches the performance of iterative refinement baselines with significantly reduced overhead. The method\u2019s effectiveness is demonstrated by recovering accurate physical observables for liquid water from unconverged reference data, including diffusion coefficients. 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