An apparatus and method are described for implementing flexible finite differences in a graphics processor. For example, one embodiment of a graphics processor comprises: pixel shading logic to perform pixel shading operations on pixels associated with a rasterized primitive using covered pixels and uncovered pixels; and helper pixel selection logic to select helper pixels in the rasterized primitive, the helper pixels to be used by the pixel sharing logic for gradient computations, wherein for one or more of the covered pixels, the helper pixel selection logic attempts to identify one or more suitable covered helper pixels and, if no suitable covered helper pixels exist, identifies one or more uncovered helper pixels.