Deep neural networks~(DNNs) have proven powerful for denoising, but they are ultimately of limited use in high-noise settings, such as for cryogenic electron microscopy~(cryo-EM) projection images. In this setting, however, datasets contain a large number of projections of the same molecule, each taken from a different viewing direction. This redundancy of information is useful in traditional denoising techniques known as class averaging methods, where images are clustered, aligned, and then averaged to reduce the noise level. We present a neural network architecture based on transformers that extends these class averaging methods by simultaneously clustering, aligning, and denoising cryo-EM images. Results on synthetic data show accurate denoising performance using this architecture, reducing the relative mean squared error (MSE) single-image DNNs by $45\%$ at a signal-to-noise (SNR) of $0.03$.