```python
def generate_integers(a, b):
    """
    Given two positive integers a and b, return the even digits between a
    and b, in ascending order.

    For example:
    generate_integers(2, 8) => [2, 4, 6, 8]
    generate_integers(8, 2) => [2, 4, 6, 8]
    generate_integers(10, 14) => []
    """
    # Determine the range (min to max)
    low = min(a, b)
    high = max(a, b)
    
    # Even digits are 0, 2, 4, 6, 8
    even_digits = [0, 2, 4, 6, 8]
    
    # Filter even digits that fall within [low, high]
    result = [d for d in even_digits if low <= d <= high]
    
    return result
```