Preheat oven to 350 degrees F (175 degrees C). Grease a loaf pan.
Beat sugar and applesauce together in a bowl with an electric mixer; add pureed bananas, yogurt, egg, and vanilla and beat until well-combined.
Whisk flour, xanthan gum, baking powder, and baking soda together in a bowl. Add flour mixture to applesauce mixture and stir until just combined. Fold chocolate chips and walnuts into batter. Spoon batter into the prepared loaf pan.
Bake in the preheated oven until a toothpick inserted in the center of the loaf comes out clean, about 45 minutes.