Answer: For readers who might not know the terms let's get some background detail: an augmented interval is expanded one half step from major or perfect, a diminished interval is reduced a half-step from major or perfect. This refers to the note names: C to E forms a major third (it covers three letter names, so it's a third), C to E# would be an augmented third - which on a piano would sound the same as a perfect fourth, C to F. Octaves, fifths, and fourths can be perfect, diminished, or augmented. Seconds, thirds, sixths, and sevenths can be major, minor, diminished, or augmented.

Leonard Meyer wrote a good book, Emotion and Meaning in Music, in which he explains the "sad" associations of minor in a way that suggests an answer to your question. He says that we tend to assume "calm contentment" and "gentle joy" to be normal emotional states and associate these with the simplest of musical modes, the major. Minor modes, he suggests, involve chromatic movement and more complex harmony and thus are unconsciously taken to imply emotional states we regard as non-normal: anguish, misery, etc.

Using that line of reasoning, both augmented and diminished intervals would be associated with the minor emotional affect. Of course, some of them will be enharmonically equivalent to major intervals as described above (a diminished fourth being played on the same piano keys as a major 3rd, for example), but in context they will still be part of a more complex and "difficult" harmonic language, and by Meyer's theory will fall into the anguish category. Sounds reasonable to me.