We propose an image-conditioned diffusion model to estimate high angular resolution diffusion weighted imaging (DWI) from a low angular resolution acquisition. Our model, which we call QID$^2$, takes as input a set of low angular resolution DWI data and uses this information to estimate the DWI data associated with a target gradient direction. We leverage a U-Net architecture with cross-attention to preserve the positional information of the reference images, further guiding the target image generation. We train and evaluate QID$^2$ on single-shell DWI samples curated from the Human Connectome Project (HCP) dataset. Specifically, we sub-sample the HCP gradient directions to produce low angular resolution DWI data and train QID$^2$ to reconstruct the missing high angular resolution samples. We compare QID$^2$ with two state-of-the-art GAN models. Our results demonstrate that QID$^2$ not only achieves higher-quality generated images, but it consistently outperforms the GAN models in downstream tensor estimation across multiple metrics. Taken together, this study highlights the potential of diffusion models, and QID$^2$ in particular, for q-space up-sampling, thus offering a promising toolkit for clinical and research applications.