Gradient with colours outside the straight axis

Another Option (not necessarily a better one than the ones already mentioned) would be using the Properties Panel to blur Layer Masks (or even Vector Masks) on Solid Color Layers (with Layer Styles like »Outer Glow« if necessary) in 16bit and adding the noise with the Layer Style »Pattern Overlay«. 

I prefer the variants suggested by @Stephen Marsh  because you can convert layers to Smart Objects and apply Gaussian Blur, then adjust the blur strength later. You can work with layers, experiment with their order, and even use layer effects like Color Overlay or Gradient Overlay applied to Smart Objects.

Another option is to paint large blocks of colour and then apply Gaussian and or motion blur.

Try adding a Gradient Map Adjustment Layer, and paint various shades of gray with a soft brush, on the layer below.