Generative models have emerged as powerful tools for producing complex objects such as images, molecules and proteins. Their practical value, however, depends not only on generating plausible samples, but also on whether they can be effectively steered toward the goals of a given scientific task. Existing steering approaches commonly optimize the average quality of generated samples. In many applications, particularly in scientific discovery, the average quality is not of primary interest. Practical objectives may instead involve enriching high-performing samples, limiting the probability of undesirable outcomes, or maintaining robust performance under distribution shift. This project aims to establish principled and efficient methods for steering generative models toward such scientifically meaningful distributional goals. The project will pursue three closely connected aims: developing computationally efficient methods for tail-aware, constraint-aware, and robustness-aware generation. The project will formulate the scientific goals as optimization objectives or constraints on the generated probability distribution. Efficient algorithms will be designed to solve such distributional optimization problems. The proposed methods will be evaluated on molecular and protein design benchmarks