# DnNP: Denoising Input Uncertainty in Neural Processes

**Authors:** Fatemeh Tohidian, Chengzhi Shi, Soomi Lee, Matthew Elia, Amy Mueller, Stratis Ioannidis, Jennifer Dy  
**Published:** 10 Nov 2026  
**Links:** [arXiv](https://arxiv.org/abs/2611.14424) · [PDF](https://arxiv.org/pdf/2611.14424) · [This page](https://omen-bit.github.io/ai-paper-daily/paper/2611.14424.html)

## Key numbers

- **30%**: DnNP reduces RMSE by up to 30% and NLL by up to 73% relative to standard…
- **73%**: …reduces RMSE by up to 30% and NLL by up to 73% relative to standard NPs.

## Abstract

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 PM2.5 spatial interpolation from real-world air quality sensors, DnNP reduces RMSE by up to 30% and NLL by up to 73% relative to standard NPs. We also provide theoretical grounding: we show that the Bayes-optimal predictor under noisy inputs belongs to the DnNP model class, and that plug-in models with fixed observation variance incur an irreducible KL divergence gap that DnNP provably avoids.

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