I regret eating so much junk food. = right I regret to eat so much junk food. = wrong When used to look back on something in the past, the verb 'regret' has to be followed by a gerund. If you regret doing something, this means that you did something and now wish that you hadn't done it e.g. "I regret drinking that tenth beer last night." You cannot use an infinitive in this context. The only time we use 'regret' with an infinitive is in the formal and formulaic "I regret to tell you that... " or "I regret to inform you that... ". This is forward-looking, and is a different meaning of the word. It's a set phrase which means 'Unfortunately, it is my duty to tell you'. I hope that makes sense.

Both sentences are grammatically fine. The second - as has been noted sounds strange but is fine technically. There is a GENERAL rule you can apply when choosing between gerund and infinitive here: The infinitive denotes a second action. The gerund denotes an object of the main verb (it is a noun -activity- after all!... not an action!) So... I regret to tell you (2 actions) I regret telling you (1 action about 1 object activity) More I stoppped smoking (1 action regarding an activity) I stopped to smoke (2 actions: stop then smoke) This leads to the possibility of such phrases as... I don't like doing my homework so I like to do my homework as soon as I get home (to get it out of the way). [CLUMSY / UNNATURAL WORDING ] I don't like the activity so I like (prefer) to do it in this way. Back to your question... I regret eating... this means you regret an activity DONE. In the past. I regret to eat... this means you regret an action that is going to happen after.. so the future! Now the question is: Which meaning are you trying to communicate?

The first is correct, the 2nd is awkward. The 2nd is more natural if you reworded it as, "I regret that I eat so much junk food".

"I regret eating so much junk food" is the more comfortable, natural way of saying this. The listener understands that eating took place in the past. "I regret to eat" sounds present and overly formal, like in the phrase "I regret to inform you", as if you are currently eating the junk food as you speak. It is weird to say it this way.