Hi M.,
Just take away the diapers during the day. It's the only way. Tell him in a matter-of-fact way that since he is a big boy now, he will only be making his pee and poop in the potty. In order to kick off this process, pick a weekend when you can be at home, and let him run around naked from the waist down. Run him to the potty constantly - every 15-20 minutes at first. Praise him when he gets it right, and when he pees on the floor, don't get mad, but say, "Next time you'll make it to the potty, since you're a big boy." I did this with both of my girls and they were potty trained in a couple of days. The fact that he knows when he needs to go, says that he's ready for potty training.
Don't wait or it will only get harder. You were right on to start it early, and now is the time to help him master this important skill! I've always felt that waiting for kids to be "ready" - in other words, making them figure it out on their own - is insulting to small children. It's like saying, "I think you're too dumb to get it so I'm not going to teach you, and you'll have to sit there in a diaper of poop in the meantime." I know that is not a popular view these days, but do you ever wonder why kids before the 80's were all potty trained at or before 2 years?? It's because their mothers taught them, plain and simple. You can do it - just stick with it and don't give up!!
THAT being said, night time is a different story. Kids can't always control that until later. My older daughter wet her bed until about 4.5 years old (my husband was a bed wetter as a child, too). She was so horrified when she'd wake up with a wet pull-up - she truly wanted to get it right, but was just such a heavy sleeper that she didn't wake up in time. My younger daughter mastered daytime and night time potty training all at once. So - when his pull-ups are dry pretty consistently in the mornings, take them away. Until then, just deal with daytime potty training.
Good luck! Potty training is a hassle, but it will be over quickly!