Yes, such a program exists!

ImageMagick has the compare utility, which has several ways of comparing images.

To install it:

sudo apt-get install imagemagick imagemagick-doc

Comparing two images visually:

compare -compose src tux_orig.png tux_modified.png tux_difference.png

tux_orig.png & tux_modified.png

Gives this image:

Comparing two images via metrics:

There are also many ways to output the differences via some metrics, e.g.:

# compare -verbose -metric PSNR tux_orig.png tux_modified.png tux_difference.png

tux_orig.png PNG 200x232 200x232+0+0 8-bit sRGB 20.6KB 0.000u 0:00.000

tux_modified.png PNG 200x232 200x232+0+0 8-bit sRGB 22.2KB 0.010u 0:00.000

Image: tux_orig.png

  Channel distortion: PSNR

    red: 19.5485

    green: 19.5973

    blue: 19.6507

    alpha: 16.1568

    all: 18.4517

tux_orig.png=>tux_difference.png PNG 200x232 200x232+0+0 8-bit sRGB 12.3KB 0.030u 0:00.020

Some metric options:

AE     absolute error count, number of different pixels (-fuzz effected)

FUZZ   mean color distance

MAE    mean absolute error (normalized), average channel error distance

MEPP   mean error per pixel (normalized mean error, normalized peak error)

MSE    mean error squared, average of the channel error squared

NCC    normalized cross correlation

PAE    peak absolute (normalize peak absolute)

PSNR   peak signal to noise ratio

RMSE   root mean squared (normalized root mean squared)

There are many ways to compare images, see ImageMagicks section on compare for further methods.