Combining multiple modalities carrying complementary information through multimodal learning (MML) has shown considerable benefits for diagnosing multiple pathologies. However, the robustness of multimodal models to missing modalities is often overlooked. Most works assume modality completeness in the input data, while in clinical practice, it is common to have incomplete modalities. Existing solutions that address this issue rely on modality imputation strategies before using supervised learning models. These strategies, however, are complex, computationally costly and can strongly impact subsequent prediction models. Hence, they should be used with parsimony in sensitive applications such as healthcare. We propose HyperMM, an end-to-end framework designed for learning with varying-sized inputs. Specifically, we focus on the task of supervised MML with missing imaging modalities without using imputation before training. We introduce a novel strategy for training a universal feature extractor using a conditional hypernetwork, and propose a permutation-invariant neural network that can handle inputs of varying dimensions to process the extracted features, in a two-phase task-agnostic framework. We experimentally demonstrate the advantages of our method in two tasks: Alzheimer’s disease detection and breast cancer classification. We demonstrate that our strategy is robust to high rates of missing data and that its flexibility allows it to handle varying-sized datasets beyond the scenario of missing modalities. We make all our code and experiments available at github.com/robustml-eurecom/hyperMM .