Inflation doesn't happen here. Bad debts actually take money out of the system. Recapitalizing the banks just add back the destroyed money.
Modern monetary policies don't "print" money anymore. Debt creation and destruction are used as the primary mean to create and destroy money. Below is a very simplified version of money creation, skipping many other aspects.
The banks lend their deposit out to the public and money is created out of the thin air and starts to circulate in the system. The banks are regulated by the central bank to maintain a certain reserve ratio on the deposit so there is a maximum level that can be lent out and that becomes the limit on the money supply. When loans are paid back, the money is destroyed but the returned money can be lent out again thus the money supply is not changed.
Central banks can influence the money supply by setting the interest rate. Lowering rate causes more loans to be made thus expanding the money supply, conversely for raising rate.
Now when a loan has gone bad, there is no money paid back to the bank. The bank is short of that amount of money. It still has to maintain the reserve ratio and can't lend that much out again. The money is gone; essentially it has been destroyed from the system.
So a bad loan actually shrinks the money in circulation, lowering the money supply. Too many bad loans would cause a credit crunch - the banks simply can't get the loan money back to re-lend them out and thus there's not enough money to go around.
Here's where the central banks step in. They recapitalize the banks (fancy word to create money out of the thin air), by either giving created money to the banks to write off the bad loans, or in the U.S. case in 2008 the Fed buying the bad debts from the banks with new money it created out of the thin air. In either case the banks get money for getting rid off the bad debts and can lend again, re-balancing the money taken out of the system due to bad debts. Thus the money supply is back to normal and life goes on.
The bad debts held by the central banks are simply some numbers on some papers, whose value are questionable. Someday it might be decided that they are worthless and, puff, they are gone.
The Chinese central bank is basically using the same mechanisms to deal with bad debts.