DnNP: Denoising Input Uncertainty in Neural Processes

Neural Processes (NPs) are flexible meta-learning models capable of uncertainty quantification across diverse applications. However, the standard NP framework assumes access to noise-free inputs. This is unrealistic in many practical settings, where sensor noise or measurement errors are unavoidable. This discrepancy between model assumptions and real-world data can significantly degrade prediction quality and uncertainty estimates. We introduce Denoising Neural Processes (DnNPs), a principled extension of the NP framework that explicitly models input uncertainty. We train DnNPs via variational inference. DnNPs jointly learn to denoise corrupted inputs and perform meta-learning, making them robust to noisy training data. We demonstrate DnNPs' effectiveness on both synthetic and real-world datasets, showing consistent improvements in prediction and uncertainty quantification compared to standard NPs. On PM$_{2.5}$ spatial interpolation from real-world air quality sensors, DnNPs reduces RMSE by up to 43% and NLL by up to 80% relative to standard NPs. We also provide theoretical grounding: we show that the Bayes optimal predictor under noisy inputs belongs to the DnNPs model class, and that plug-in models with fixed observation variance incur an irreducible KL divergence gap that DnNPs provably avoids.