Most self-supervised learning objectives defend against collapse but leave the target representation law unspecified. We formulate representation learning as Distribution Matching (DM), learning an augmentation-invariant encoder whose push-forward law matches an explicit reference law. The reference law specifies what the learned representation distribution should look like, while the matching mechanism determines how this target is matched. Within DM, generative learning and representation learning can be viewed as directionally inverse distributional processes: generative learning maps a tractable reference to data, whereas representation learning maps data to a designed reference law. For the Mallows-distance instantiation studied here, we connect the population objective to class-centre separation and classification error and derive a finite-sample bound on downstream classification error. Simulations and image benchmarks show manifold rectification, fine-grained structure and transferability.

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