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While it has long been known in statistics that not accounting for such errors can produce a substantial bias, the vast majority of deep learning models have thus far neglected Errors-in-Variables approaches. Reasons for this include a significant increase of the numerical burden and the challenge in assigning an appropriate prior in a Bayesian treatment. To date, the attempts made to use Errors-in-Variables for neural networks do not scale to deep networks or are too simplistic to enhance the prediction performance. This work shows for the first time how Bayesian deep Errors-in-Variables models can increase the prediction performance. We present a scalable variational inference scheme for Bayesian Errors-in-Variables and demonstrate a significant increase in prediction performance for the case of image classification. Concretely, we use a diffusion model as input posterior to obtain a distribution over the denoised image data. We also observe that training the diffusion model on an unnoisy surrogate dataset can suffice to achieve an improved prediction performance on noisy data.<\/jats:p>","DOI":"10.1007\/s10994-025-06744-x","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T22:06:52Z","timestamp":1740434812000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Deep Errors-in-Variables using a diffusion model"],"prefix":"10.1007","volume":"114","author":[{"given":"Josua","family":"Faller","sequence":"first","affiliation":[]},{"given":"J\u00f6rg","family":"Martin","sequence":"additional","affiliation":[]},{"given":"Clemens","family":"Elster","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,24]]},"reference":[{"key":"6744_CR1","doi-asserted-by":"crossref","unstructured":"Bassu, D., Lo, J.T. & Nave, J. (1999). 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None of the experiments in this paper involves animals, plants, or human entities.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"Not applicable. The paper does not include data or images requiring permissions.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The code to reproduce these experiments is provided at\u00a0.","order":6,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}],"article-number":"107"}}