Is it safe?

Sarah • 27. Married. My son was born 2/22/16 and his little sister 7/5/17
I have always struggled with food/binge eating- I struggled from bulimia as a teen, and recovered, partially, I stil have an episode a few times a week of just simply binging, I've gained 50 lbs in nearly a year! So I got on track and started working out and eating better... I have now discovered I am pregnant. I would by no means restrict
My body of food because well, I'm providing for a growing baby! However, eating better and working out, I will probably lose a lot of weight simply by not binging- is losing a lot of weight safe for the baby? Even if the weight loss is done in a healthy way?