Point cloud extraction (PCE) and ego velocity estimation (EVE) are key capabilities gaining attention in 3D radar perception. However, existing work typically treats these two tasks independently, which may neglect the interplay between radar's spatial and Doppler domain features, potentially introducing additional bias. In this paper, we observe an underlying correlation between 3D points and ego velocity, which offers reciprocal benefits for PCE and EVE. To fully unlock such inspiring potential, we take the first step to design a Spatial-Doppler Diffusion (SDDiff) model for simultaneously dense PCE and accurate EVE. To seamlessly tailor it to radar perception, SDDiff improves the conventional latent diffusion process in three major aspects. First, we introduce a representation that embodies both spatial occupancy and Doppler features. Second, we design a directional diffusion with radar priors to streamline the sampling. Third, we propose Iterative Doppler Refinement to enhance the model’s adaptability to density variations and ghosting effects. Extensive evaluations show that SDDiff significantly outperforms state-of-the-art baselines by achieving 59% higher in EVE accuracy, 4X greater in valid generation density while boosting PCE effectiveness and reliability. The code and dataset will be available on https://github.com/StellarEsti/SDDiff.