Efficient compression of low-bit-rate point clouds is critical for bandwidth-constrained applications. However, existing techniques mainly focus on high-fidelity reconstruction, requiring many bits for compression. This paper proposes a "Denoising Diffusion Probabilistic Model" (DDPM) architecture for point cloud compression (DDPM-PCC) at low bit-rates. A PointNet encoder produces the condition vector for the generation, which is then quantized via a learnable vector quantizer. This configuration allows to achieve a low bitrates while preserving quality. Experiments on ShapeNet and ModelNet40 show improved rate-distortion at low rates compared to standardized and state-of-the-art approaches. We publicly released the code at https://github.com/EIDOSLAB/DDPM-PCC.