Large genomic and imaging datasets can be used to train models that learn meaningful representations of cellular systems. Across domains, model performance improves predictably with dataset size and compute budget, providing a basis for allocating data and computation. Scientific data, however, is also limited by noise arising from factors such as molecular undersampling, sequencing errors, and image resolution. By fitting 1,670 representation learning models across three data modalities (gene expression, sequence, and image data), we show that noise defines a distinct axis along which performance improves. Noise scaling follows a logarithmic law. We derive the law from a model of noise propagation, and use it to define noise sensitivity and model capacity as benchmarking metrics. We show that protein sequence representations are noise-robust while single cell transcriptomics models are not, with a Transformer-based model showing greater noise robustness but lower saturating performance than a variational autoencoder model. Noise scaling metrics may support future model evaluation and experimental design.