Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts. To be robust to outliers and differences in scale across features, a matrix factorization step is usually preceded by ad-hoc feature normalization steps, such as tf-idf scaling or data whitening. We propose in this work to learn these normalization operators jointly with the factorization itself. More precisely, given a d× n matrix X of d features measured on n individuals, we propose to learn the parameters of quantile normalization operators that can operate row-wise on the values of X and/or of its factorization UV to improve the quality of the low-rank representation of X itself. This optimization is facilitated by the introduction of differentiable quantile normalization operators derived using regularized optimal transport algorithms.