BSO: Safety Alignment Is Density Ratio Matching

Aligning language models for both helpfulness and safety typically requires complex pipelines---separate reward and cost models, online reinforcement learning, and primal-dual updates. Recent direct preference optimization approaches simplify training but incorporate safety through ad-hoc modifications such as multi-stage procedures or heuristic margin terms, lacking a principled derivation. We show that the likelihood ratio of the optimal safe policy admits a closed-form decomposition that reduces safety alignment to a density ratio matching problem. Minimizing Bregman divergences between the data and model ratios yields Bregman Safety Optimization (BSO), a family of single-stage loss functions, each induced by a convex generator, that provably recover the optimal safe policy. BSO is both general and simple: it requires no auxiliary models, introduces only one hyperparameter beyond standard preference optimization, and recovers existing safety-aware methods as special cases. Experiments across safety alignment benchmarks show that BSO consistently improves the safety--helpfulness trade-off.