This is merely my own interpretation of what was happening with No Face over the course of the movie. This bears no real application to anything. I still don't know exactly what No Face is, but it seems like he was fine and dandy up until actually getting into the bathhouse, and there are a few lines that hint that his nature is to be influenced by strong negative emotions. (Yubaba saying that the employee's greed attracts all kinds of customers, and Chihiro saying that being in the bathhouse seems to make him crazy.)
No Face, they called him. He was unwanted among the spirits. An outsider. A monster. He rarely showed himself before others, preferring to watch, invisibly, as they carried about their day. He was lonely. So lonely. And yet… the human girl. She had called to him. Invited him inside. She was different. And outsider. A human. Her kindness touched him, and he followed her, helped her. He would give her anything she wanted. Anything in the world.
But the bathhouse was poisonous. The greed of those working in it spilled into his body from every direction. Made him hungry. Filled him with lust. Still, he tried to get close to her, helping her by giving her bath tokens when the foreman would not allow it. But she rejected his kindness. Was this not what she wanted? She only wanted one. The tokens slipped from his grasp as he faded from her sight to contemplate what she wanted. If only he knew, he would give it to her.
He watched her struggle with removing the pollution from the river spirit. Saw the frantic actions of the employees, scrabbling over the gold it left behind. It corrupted him, twisted him. He took the gold into himself, and it became him. Using the gold, he lured in an employee, his own greed swelling, and devoured him, absorbing his abilities. His body morphed, and he could speak his desires now. Sen? He vaguely remembered, but he was so very hungry. He lured the next employee, blatantly announcing his desire to eat everything. And they brought everything before him, begging for gold. Their greed became his greed, and it could not be controlled.
And then, he saw her, desperately trying to go somewhere. He caught up to her, and his hands filled with gold. Surely, she would want this too, and he would give it to her. As much as she wanted. He offered it to her, finding himself unable to speak, overwhelmed by the desire to make her happy. And again, he was rejected. Greed, resentment, all the negative emotions around him, flooded into him in his shock, and the gold shook right out of his hands as he watched her leave. If she didn't want the gold, nor the tokens, what did she want!? He devoured two more people. They attempted to contain him in a room, bringing ever more food for him to devour. It was not enough. It would never be enough! He wanted her. He wanted Sen!
She came back to him. His Sen came back to him. Why was she just sitting there? Why wouldn't she smile at him, or speak? He offered her food. He tried to give her more gold, it was for her, and nobody else. She refused it once again. He asked her what she desired. Promised anything. He could make it happen. He would make it happen. If she would only tell him what she wanted! But she only asked to leave. And then, she offered him something. He took it, and began to vomit up all of the things inside of him. His warped emotions turned to rage, and he chased her through the bathhouse, growing smaller, the negative emotions he had soaked up slowly being expunged along with the things coming up.
She called to him as the last of what he had eaten was finally brought up. His head was clear. The greed no longer warped him. He followed her, wanting only to be close again. She still accepted him, even after his rampage. She even invited him to come with her, even to sit next to her on the train. At Swamp Bottom, Zeniba was warm. There was no greed to warp him. Sen and Zeniba were good people, and they both accepted him. He could be helpful here. He was wanted, and even appreciated. Sen even thought of him as a friend. He waved goodbye to Sen, no, Chihiro was her real name, as she rode off on Haku's back, for the first time feeling like he belonged. Maybe he didn't have to be a monster after all.