A model generation system generates three-dimensional object models based on two-dimensional images of an object. The model generation system can apply an iterative gradient decent process to model parameters for part models within an object model to compute a final set of model parameter values to generate the object model. To compute the final set of model parameter values, the model generation generates a reference image of the object model and compares the reference image to a received image. The model generation system uses a differentiable error function to score the reference image based on a received image. The model generation system updates the set of model parameter values based on the score for the reference image, and iteratively repeats the process until a reference image is sufficiently similar to the received image.