Predicting stable and metastable structures is central to molecular and materials discovery, but remains limited by the cost of searching high-dimensional energy landscapes. Deep generative models offer efficient structure sampling, yet their outputs remain shaped by training data and can underexplore minima that are rare but physically relevant. We introduce generative structure search (GSS), a unified framework that formulates diffusion-based generation and random structure search (RSS) as limiting regimes of a common sampling process driven by learned score fields and physical forces. Coupling these drivers lets GSS use data priors to accelerate sampling while retaining energy-guided exploration of local minima. Across molecular and crystalline systems, GSS recovers diverse metastable structures with more than tenfold lower sampling cost than RSS for broad coverage and remains effective for compositions outside the training distribution. The results establish a physically grounded generative search strategy for discovering structures beyond the reach of data-driven sampling alone.