The German automaker is expected to tell a federal judge in San Francisco Thursday that it has agreed to offer to buy back up to 500,000 2.0-liter diesel U.S. vehicles that used sophisticated software to evade U.S. emission rules.

Volkswagen has also agreed to a compensation fund for owners, but it is not clear how much owners might receive, a person briefed on the matter said.

Volkswagen may also offer to repair polluting diesel vehicles if U.S. regulators approve the fix as workable at a future date, the sources said.

VW will pay cash compensation to owners who either sell their vehicles back or get them fixed, a source briefed on the matter said. Owners selling back their vehicles will get an additional cash payment on top of receiving the estimated value of the vehicles from before the emissions scandal became public in September 2015.

The compensation fund is expected to represent more than $1 billion on top of the cost of buying back the vehicles, a person briefed on the matter said.

Owners are expected to have around two years to decide whether to sell back vehicles or get them repaired. It is not clear whether VW will be allowed to resell vehicles they buy back, the source said.

A VW spokeswoman, the EPA and the Justice Department declined to comment Wednesday.

Separately, Germany’s Die Welt newspaper reported Wednesday that the deal to settle the case would involve it paying each affected customer $5,000. But a person briefed on the matter said no decisions on how individual compensation will be awarded have been made.

In December, VW said it was creating an independent claims program for owners of vehicles with excess emissions.

It named compensation expert Ken Feinberg, who administered funds for the Sept. 11, 2001 attacks, BP Plc Deepwater Horizon oil spill and General Motors Co ignition switch crashes, to create and administer the program.

The framework deal with U.S. officials was reached after lengthy talks in recent days at the Washington law office of Robert Mueller, the former FBI director and court appointed mediator named to help settle more than 500 civil suits.

Some elements of the settlement are still being worked out and details are not expected to be announced Thursday at a court hearing.

A final settlement is also expected to include an environmental remediation fund to address excess pollution emitted by the vehicles since 2009. It is not clear if the deal will resolve the Justice Department’s civil suit filed in January against VW or if VW will agree to pay a civil penalty.

U.S. District Judge Charles Breyer in March gave VW until Thursday “to announce a concrete proposal for getting the polluting vehicles off the road.”

Breyer said in March the “proposal may include a vehicle buy-back plan or a fix approved by the relevant regulators that allows the cars to remain on the road with certain modifications.”

In September VW admitted to cheating on emissions tests for 11 million vehicles worldwide since 2009, which prompted VW Chief Executive Martin Winterkorn to resign.

VW still faces ongoing criminal investigations by the U.S. Justice Department and other prosecutors around the world.