Increasing Resolution of Image By Splitting Image Pixel into Smaller Pixels | Google Earth Engine?

I have two MODIS satellite images with same custom band, one of 1000m/px resolution and other of 250m/px. I want to compute their mean ‘image’ and display as map layer.

My current way of achieving this is as follows:

var img_col = ee.ImageCollection(img_1.select('DP1'), img_2.select('DP1));
img_col = img_col.mean();
Map.addLayer(img_col, params_obj);

But this does not result in raster image with 250m/px resolution. How to specifically generate image with resolution equal to the highest of two initial images?