In this paper, we propose a novel score-base generative model for unconditional raw audio synthesis. Our proposal builds upon the latest developments on diffusion process modeling with stochastic differential equations, which already demonstrated promising results on image generation. We motivate novel heuristics for the choice of the diffusion processes better suited for audio generation, and consider the use of a conditional U-Net to approximate the score function. While previous approaches on diffusion models on audio were mainly designed as speech vocoders in medium resolution, our method termed CRASH (Controllable Raw Audio Synthesis with High-resolution) allows us to generate short percussive sounds in 44.1kHz in a controllable way. Through extensive experiments, we showcase on a drum sound generation task the numerous sampling schemes offered by our method (unconditional generation, deterministic generation, inpainting, interpolation, variations, class-conditional sampling) and propose the class-mixing sampling, a novel way to generate "hybrid" sounds. Our proposed method closes the gap with GAN-based methods on raw audio, while offering more flexible generation capabilities with lighter and easier-to-train models.