Ulysses takes place in the course of one day, from 8am on June 16th to sometime after 4 A.M. on June 17th. People often joke about the fact that nothing happens in Ulysses. We readily admit that if all the book did was narrate the actions of the characters, it'd be pretty boring and you'd probably never had heard of it. But Ulysses does more. Much more. With the intimate view that we get of each character's inner life, we are exposed to the vast expanse of their memories. Events in the present inevitably make them think of the past. The book poses a lot of big questions about the relation of past to present, particularly in terms of happiness: is remembered happiness somehow inferior to happiness experienced first-hand?
In Joyce's novel, painful memories, such as Stephen's memory of the death of his mother, tend to be involuntary – they take possession of the characters without their control. Pleasant memories, on the other hand, seem to be voluntary – they are actively conjured up by the characters to make themselves feel better.
Molly's memory of Bloom's proposal at the end of the novel is a re-affirmation of their marriage, and in this case the act of remembering is an act of making past feelings and convictions present.