Distribution alignment can be used to learn invariant representations with applications in fairness and robustness. Most prior works resort to adversarial alignment methods but the resulting minimax problems are unstable and challenging to optimize. Non-adversarial likelihood-based approaches either require model invertibility, impose constraints on the latent prior, or lack a generic framework for alignment. To overcome these limitations, we propose a non-adversarial VAE-based alignment method that can be applied to any model pipeline. We develop a set of alignment upper bounds (including a noisy bound) that have VAE-like objectives but with a different perspective. We carefully compare our method to prior VAE-based alignment approaches both theoretically and empirically. Finally, we demonstrate that our novel alignment losses can replace adversarial losses in standard invariant representation learning pipelines without modifying the original architectures -- thereby significantly broadening the applicability of non-adversarial alignment methods.

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