We propose a deep learning method for 3D volumetric reconstruction in low-dose helical cone-beam computed tomography. Prior machine learning approaches require reference reconstructions computed by another algorithm for training. In contrast, we train our model in a fully self-supervised manner using only noisy 2D X-ray data. This is enabled by incorporating a fast differentiable CT simulator in the training loop. As we do not rely on reference reconstructions, the fidelity of our results is not limited by their potential shortcomings. We evaluate our method on real helical cone-beam projections and simulated phantoms. Our results show significantly higher visual fidelity and better PSNR over techniques that rely on existing reconstructions. When applied to full-dose data, our method produces high-quality results orders of magnitude faster than iterative techniques.