How long could it take swelling in leg to go down after DVT diagnosis and warfarin started?

Several months. After starting warfarin the blood clot can no longer grow. The body will start to break down the clot within days. It takes months to have the clot reabsorbed or for the process to make an opening through the clot so blood can get through again. Swelling will be visibly less in a few weeks but it could be 6 months before the leg is back to normal. Occasionally, the swelling persists indefinitely.
Could be permanent. I agree with dr. Smith. It can take months. Wearing compression stockings right away will help but it is essential to wear the stockings for at least wo years to help to decrease your chance that the swelling might never go away.
Secondary lymphedema. The swelling is caused by secondary lymphedema if you see a lymphedema therapist who can do manual lymph drainage and complex decongestive therapy - a special wrapping of legs swelling will go away within a week.