Despite recent advances, self-supervised learning (SSL) models and Joint-Embedding Predictive Architectures (JEPAs) remain susceptible to spurious correlations. Many anti-collapse regularizers constrain the global representation distribution to match a prescribed target, such as a multivariate Gaussian or the uniform distribution on the sphere. However, global matching does not prevent groups defined by a bias attribute from occupying distinct regions of the representation space. We show that existing encoder-only debiasing regularizers, including EnD and FSCL, can be interpreted as restricted forms of conditional distribution matching. Building on this interpretation, we introduce Unbiased Open World (UOW), which matches the representation distribution within each observed bias group to a common target distribution. At the population optimum, using a discriminative conditional discrepancy guarantees independence between the representation and the targeted attribute. We instantiate UOW in Gaussian and spherical spaces and evaluate it across controlled synthetic settings and real-world fairness benchmarks. Across Synthetic Engraving, Colored MNIST, CelebA, and Waterbirds, conditional matching substantially reduces bias compared with global regularization while preserving useful downstream representations. Jointly conditioning on multiple bias attributes further reduces intersectional disparities missed by separate marginal constraints. Finally, experiments on CelebA show that models can be trained from random initialization using UOW as a pretraining objective, provided checkpoints are selected according to fairness-aware validation criteria.

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