While running won't specifically target face fat, it can contribute to overall weight loss, which may lead to a slimmer face. Running, like other forms of cardio, helps burn calories and reduce body fat.
As your body fat decreases, you'll likely see a reduction in fat throughout your body, including your face. However, you can't spot reduce fat; it's impossible to target fat loss in specific areas.
Remember that everyone loses weight differently, and some people may notice a more significant change in their face than others.
For a comprehensive approach to slimming your face, consider incorporating healthy eating habits, adequate hydration, and other forms of exercise into your routine.
