My guess is that the old KGB man has no interest in peace, even on the most favorable terms. What he wants is to stay in power at home. And while victories help to shore him up, ongoing conflicts are even better.
Autocrats depend on public opinion. They may not have to worry about elections, but they need a critical mass of public support to sustain their regimes. Putin knows how to use foreign quarrels to shore up his position, keeping Russian voters in a state of high-octane, patriotic anxiety.
I'd like to clarify that statement on ongoing conflict benefiting Putin. I think Putin has an interest in an ongoing conflict that doesn't cost him much in lives or money.
So I'd help Ukraine send body bags back to Russian mothers. Then we'll see how much the thrill of foreign victories bolsters Putin's standing. Then maybe Putin will have an interest in real peace with Ukraine.
UPDATE: Ukraine and Russia's Donbas hand puppet "separatists" will exchange prisoners. I don't know what this leads to but it won't be a Russian withdrawal from Russian-occupied Ukraine.