guess > < imagine > < visualize

Both guess and imagine can be used as verbs. As a verb 'guess' is to reach partly (or totally) a conclusion.
 Eg. If you have not come across that word, doesn't matter. Can't you guess it by the context?

 Guess is a prediction about the outcome of something.
 Eg. What is your guess, who will win Huzurnagar election?

 Whereas, imagine is to form a mental image of something in one's mind.
 Eg. Imagine yourself to be in a crowded river boat. What precautions would you take for your safety?

 Imagine as a verb is to form a mental image of something in one's mind.
 Eg. Can you imagine a car which gives 40 km per a litre of petrol?

 visualize - [విజువలైజ్] form a mental image
 Eg. I can visualize our country's technological advance in 10 years.