We propose a novel approach for reconstructing animatable 3D Gaussian avatars from monocular videos captured by commodity devices like smartphones. Photorealistic 3D head avatar reconstruction from such recordings is challenging due to limited observations, which leaves unobserved regions under-constrained and can lead to artifacts in novel views. To address this problem, we introduce a multi-view head diffusion model, leveraging its priors to fill in missing regions and ensure view consistency in Gaussian splatting renderings. To enable precise viewpoint control, we use normal maps rendered from FLAME-based head reconstruction, which provides pixel-aligned inductive biases. We also condition the diffusion model on VAE features extracted from the input image to preserve details of facial identity and appearance. For Gaussian avatar reconstruction, we distill multi-view diffusion priors by using iteratively denoised images as pseudo-ground truths, effectively mitigating over-saturation issues. To further improve photorealism, we apply latent upsampling to refine the denoised latent before decoding it into an image. We evaluate our method on the NeRSemble dataset, showing that GAF outperforms the previous state-of-the-art methods in novel view synthesis by a 5.34\% higher SSIM score. Furthermore, we demonstrate higher-fidelity avatar reconstructions from monocular videos captured on commodity devices.

We present an efficient convolution kernel for Convolutional Neural Networks (CNNs) on unstructured grids using parameterized differential operators while focusing on spherical signals such as panorama images or planetary signals. To this end, we replace conventional convolution kernels with linear combinations of differential operators that are weighted by learnable parameters. Differential operators can be efficiently estimated on unstructured grids using one-ring neighbors, and learnable parameters can be optimized through standard back-propagation. As a result, we obtain extremely efficient neural networks that match or outperform state-of-the-art network architectures in terms of performance but with a significantly lower number of network parameters. We evaluate our algorithm in an extensive series of experiments on a variety of computer vision and climate science tasks, including shape classification, climate pattern segmentation, and omnidirectional image semantic segmentation. Overall, we present (1) a novel CNN approach on unstructured grids using parameterized differential operators for spherical signals, and (2) we show that our unique kernel parameterization allows our model to achieve the same or higher accuracy with significantly fewer network parameters.