Mosaicking a Image Collection by Date (day) in Google Earth Engine

I have an image collection of Sentinel-1 data over 3 years filtered by a region of interest that spans 3-4 tiles, and want to know the best way to mosaic all the images (tiles) that were taken on the same day into one image. Currently filtering by date yields separate images for each separate tile, and I would like to merge all images (tiles) from the same day into one image.

I know how to do this for one specified date with a command like this:

ee.Image(collection.filterDate('2014-10-01','2014-10-02').mosaic())

But I would like to do this iteratively for the whole collection in my ROI over a broad date range and obtain a new image collection of mosaicked images by days in which there is some data.

The collection is created by the following code:

var poly = /* color: #d63000 */ee.Geometry.Polygon(
    [[[-76.0803, 10.8656],
      [-76.0913, 7.7436],
      [-73.1909, 7.7545],
      [-73.3776, 9.4273],
      [-75.2124, 10.9304]]])

var start = ee.Date('2014-10-01');
var finish = ee.Date('2018-03-31');

var collection = ee.ImageCollection('COPERNICUS/S1_GRD')
.filterDate(start, finish)
.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))
.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
.filter(ee.Filter.eq('instrumentMode', 'IW'))
.filterMetadata('resolution_meters', 'equals', 10)
.filterBounds(poly);

For example, the first three images in this collection are all tiles from the same day (2014-12-02), and I would like to mosaic them together into one 3-tile image for day 2014-12-02, and then do this for the entire collection of over 500 tiles/images to get a collection of day-unique tile mosaics.

var poly = /* color: #d63000 */ee.Geometry.Polygon(
    [[[-76.0803, 10.8656],
      [-76.0913, 7.7436],
      [-73.1909, 7.7545],
      [-73.3776, 9.4273],
      [-75.2124, 10.9304]]])

var start = ee.Date('2014-10-01');
var finish = ee.Date('2018-03-31');

var collection = ee.ImageCollection('COPERNICUS/S1_GRD')
.filterDate(start, finish)
.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VV'))
.filter(ee.Filter.listContains('transmitterReceiverPolarisation', 'VH'))
.filter(ee.Filter.eq('instrumentMode', 'IW'))
.filterMetadata('resolution_meters', 'equals', 10)
.filterBounds(poly);

// Difference in days between start and finish
var diff = finish.difference(start, 'day')

// Make a list of all dates
var range = ee.List.sequence(0, diff.subtract(1)).map(function(day){return start.advance(day,'day')})

// Funtion for iteraton over the range of dates
var day_mosaics = function(date, newlist) {
  // Cast
  date = ee.Date(date)
  newlist = ee.List(newlist)

  // Filter collection between date and the next day
  var filtered = collection.filterDate(date, date.advance(1,'day'))

  // Make the mosaic
  var image = ee.Image(filtered.mosaic())

  // Add the mosaic to a list only if the collection has images
  return ee.List(ee.Algorithms.If(filtered.size(), newlist.add(image), newlist))
}

// Iterate over the range to make a new list, and then cast the list to an imagecollection
var newcol = ee.ImageCollection(ee.List(range.iterate(day_mosaics, ee.List([]))))
print(newcol)

function mosaicByDate(imcol){
  // imcol: An image collection
  // returns: An image collection
  var imlist = imcol.toList(imcol.size())

  var unique_dates = imlist.map(function(im){
    return ee.Image(im).date().format("YYYY-MM-dd")
  }).distinct()

  var mosaic_imlist = unique_dates.map(function(d){
    d = ee.Date(d)

    var im = imcol
      .filterDate(d, d.advance(1, "day"))
      .mosaic()

    return im.set(
        "system:time_start", d.millis(), 
        "system:id", d.format("YYYY-MM-dd"))
  })

  return ee.ImageCollection(mosaic_imlist)
}