1. An image processing device for generating output data used when an image displayed on a display device is to be output by an output device, the image processing device comprising: an output execution instruction input unit configured to input an instruction to execute image output via the output device; and a color space converter configured to carry out (i) a first conversion process that converts first device-dependent image data that expresses an image in a first device-dependent color space handled by the display device into device-independent image data that expresses the image in a device-independent color space, and (ii) a second conversion process that converts the device-independent image data into second device-dependent image data as the output data that expresses the image in a second device-dependent color space handled by the output device, wherein the color space converter initiates the first conversion process prior to an input of an instruction to execute output by the output execution instruction input unit, and initiates the second conversion process in response to the input of an instruction to execute output by the output execution instruction unit, the image processing device further comprising: a correction processer configured to correct image data, wherein the first device-dependent image data is image data resulting from correction processing by the correction processor, and the color space converter initiates the first conversion process in response to the completion of correction processing by the correction processor, wherein the correction processor can execute various types of correction processes, and the color space converter initiates the first conversion processing in response to the completion of a specified type of correction process among the various types of correction processes executed by the correction processor, the image processing device further comprising: a process history storage unit configured to, among the correction processes executed by the correction processor, record the type of correction process executed immediately prior to the input of an instruction to execute output, wherein the color space converter sets as the specified type of correction process the correction process that has been executed most frequently among the correction processes recorded in the process history storage unit.