Like this????
Easy and quick in PS 2016 and after. Bring it into PS then
1. CTRl j to make a duplicate copy on a new layer
2. With duplicate layer selected go to Filter>Convert for smart filter
3. Then with same layer selected go to Filter>Blur>Surface Blur
3. You can play with the settings for a little more if you like, but this one was set to Radius 45, Threshold 18. click >ok (By converting the layer to a smart filter, you can go back later and click on it to readjust if you need to)
4. with the layer with the blur applied, >hold down the Alt key and click mask. for black mask on the layer.
5. Go to brush. Select white as foreground. Set your brush size to the width of the transition, hardness to about 20. Opacity 100%
6. With Mask selected, brush down the line to revel the blur. Use the opacity setting on the layer to adjust the effect.