Day by day
Definition 1 of 2
Pro Tip 1/3Progress Implication
Suggests improvement or development is happening slowly over time. 
Her piano skills are increasing day by day.
Pro Tip 2/3Subtle Change
Indicates changes that may not be immediately obvious, but occur over time. 
The plants in the garden are growing day by day.
Pro Tip 3/3Optimistic Tone
Often conveys a sense of hope or positive expectation about the future. 
Their efforts are paying off day by day.