Abstract: Post hoc privacy auditing techniques can be used to test the privacy guarantees of a model, but come with several limitations: (i) they can only establish lower bounds on the privacy loss, (ii) the intermediate model updates and some data must be shared with the auditor to get a better approximation of the privacy loss, and (iii) the auditor typically faces a steep computational cost to run a large number of attacks. In this paper, we propose to proactively generate a cryptographic certificate of privacy during training to forego such auditing limitations. We introduce Confidential-DPproof , a framework for Confidential Proof of Differentially Private Training, which enhances training with a certificate of the $(\varepsilon,\delta)$-DP guarantee achieved. To obtain this certificate without revealing information about the training data or model, we design a customized zero-knowledge proof protocol tailored to the requirements introduced by differentially private training, including random noise addition and privacy amplification by subsampling. In experiments on CIFAR-10, Confidential-DPproof trains a model achieving state-of-the-art $91$% test accuracy with a certified privacy guarantee of $(\varepsilon=0.55,\delta=10^{-5})$-DP in approximately 100 hours.