In Heavy Rain, it is possible for a Madison and Ethan romance to develop over the course of the game.
When Madison first meets Ethan after The Bear Trial, she merely feels pity for him and decides to help him into his room. As they are strangers to one another, you have the choice to guide him to his room and leave or help him with his injuries. If you choose to help Ethan, he and Madison start getting to know each other.
They meet a second time after The Butterfly Trial, when Madison is passing by Ethan's motel room and realizes the door is open slightly. She peers in to see Ethan lying unconscious on the floor of his room. She helps him to his bed and treats his wounds. He slips into an unconscious state once again and Madison waits till he awakes. When Ethan awakes they talk about Madison's past and her insomnia for a short period of time, and then Madison asks Ethan why he's in such a state. Ethan quickly shrugs off the subject and asks Madison to leave.
The third time they meet, Madison follows Ethan to find out what he is up to, finding out on her way that the police are doing the same. Madison finds Ethan in a building after he completes The Lizard Trial and tells him the police are after him. Depending on the speed at which you act, Madison can help Ethan escape the police.
The fourth time they cross paths, Ethan has just completed The Shark Trial and is distraught because he either killed or couldn't kill a man to save his son. Madison sits next to Ethan and tries to explain how she knows he's not the Origami Killer. She moves in to kiss Ethan, and you can choose to kiss or not to kiss her. Kissing her will lead to a romantic relationship between the pair and eventually, you can choose whether or not you want Ethan to make love to Madison.
When Ethan wakes up the next morning he decides himself to leave without Madison and do The Rat Trial so as to not involve her any further. While picking up his coat he realizes Madison was only helping him because she wanted to write a story about him. The two have an argument, which ends with the player having to choose whether Ethan will forgive or reject Madison. This decision will affect both characters' endings.
If you do the romance scene with Madison, both Ethan and her survive, Shaun is saved, and you forgive Madison then the two will date/marry. This is shown when they buy a house, with Madison replacing Shaun's mom, Grace.
If you do the romance scene and Madison dies, Ethan is seen watching Madison's grave from afar while looking upset.
If you do the romance scene and Ethan dies, Madison will be seen watching Ethan's grave from the tree looking sad.
If you do the romance scene with Madison, both she and Ethan and survive, but Shaun dies, and you forgive Madison, Ethan will commit suicide in front of Shaun's grave. Madison will run at him in a futile attempt to stop him, and then cry over his body.