We introduce a general framework for end-to-end optimization of the rate-distortion performance of nonlinear transform codes assuming scalar quantization. The proposed framework can be used to optimize any differentiable pair of analysis and synthesis transforms in combination with any differentiable perceptual metric. As an example, we optimize a code built from a linear transform followed by a form of multi-dimensional gain control. Distortion is measured with a state-of-the-art perceptual metric. The code, optimized over a large database of images, offers substantial improvements in bitrate and perceptual appearance over fixed (DCT) codes, as well as over linear transform codes optimized for mean squared error.