We will introduce ASTRA, a generative framework that tackles transition state discovery through the inference-time steering of score-based diffusion models. We will discuss how this approach bypasses the need for prior mechanistic knowledge, using score-based interpolation as initialisation of the transition state ensemble followed by a novel Score-Aligned Ascent (SAA) method that refines these initial guesses. We will demonstrate how ASTRA successfully identifies competing pathways and first-order saddle points using only short molecular dynamics trajectories from known metastable basins as training data.