Rates on several major routes have nearly doubled over the past week, as a race for storage accelerates, according to shipping data.
For example, a 90,000 tonne cargo of diesel was booked last week out of the port of Yanbu on the west coast of Saudi Arabia to go to Europe at a lump sum of $3.975 million.
On Friday, Saudi Aramco's trading arm booked a similar cargo on the same route for $7.25 million, shipping data showed.
This equates to freight costing roughly $80 per tonne of diesel, which currently trades at around $200 a tonne.
At least 30 million barrels of jet fuel, gasoline and diesel are currently in floating storage at sea as on-land tanks are full or already booked due to a sharp drop in global consumption, according to traders and shipping data.
The growing glut of diesel, jet fuel and gasoline, among other fuels, means refineries will soon be forced to sharply reduce output or even shut down, said Robert Campbell, head of oil products analysis at consultancy Energy Aspects.
Many refiners have already cut processing rates or even shut down.
"It is an apocalyptic outcome for any refiner that is dependent on the export market to keep running," Campbell said.
The rally in freight rates for refined oil products follows sharp gains in crude oil tanker rates in recent weeks as traders store over 160 million barrels of crude offshore.