We propose DiffQ a differentiable method for model compression for quantizing model parameters without gradient approximations (e.g., Straight Through Estimator). We suggest adding independent pseudo quantization noise to model parameters during training to approximate the effect of a quantization operator. DiffQ is differentiable both with respect to the unquantized weights and the number of bits used. Given a single hyper-parameter balancing between the quantized model size and accuracy, DiffQ optimizes the number of bits used per individual weight or groups of weights, in end-to-end training. We experimentally verify that our method is competitive with STE based quantization techniques on several benchmarks and architectures for image classification, language modeling, and audio source separation. For instance, on the ImageNet dataset, DiffQ compresses a 12 layers transformer-based model by more than a factor of 8, (lower than 4 bits precision per weight on average), with a loss of 0.3% in model accuracy. Code is available at github.com/facebookresearch/diffq.