The party announced the new policy after figures published in October last year showed the UK Government gross debt reaching more than £1,876 billion - in part because of massive spending to deal with the coronavirus pandemic.
Mr Salmond, who was previously SNP leader, has urged his former party to adopt this stance on what Alba called a "clean break settlement".
The policy stands in contrast to SNP proposals published in advance of the 2014 referendum in the white paper on independence, which said that separate Scotland would take on a "negotiated and agreed" share of the UK debt.
However, Alba noted that "as a percentage of GDP the debt has doubled since the financial crisis of 2008 when the government and Bank of England embarked on wholesale quantitative easing".
Alba Party policy - which was drawn up by economist and Alba Party Central Scotland candidate Jim Walker - stated: "That debt is largely owed by one branch of government (the Treasury) to another (the central bank) and therefore forms no legitimate liability for the Scottish or any other people."
The party made clear it "rejects entirely any obligation to share debt accrued through central bank money printing and sees no role for Scotland on paying interest on that debt".
Mr Salmond said: "Austerity and coronavirus has changed the economic world and changed it utterly. Thus the independence platform must adjust to the new realities.
"They bring with them many new challenges but also great economic opportunities."
By not taking on any share of UK debt, Alba argued an independent Scotland would be able to focus resources on a economic recovery programme, with the country "free from the shackles of UK debt, or even worse still paying billions of pounds to the UK Government in some bizarre annual subvention".
The party wants Scotland to set up its own currency "as soon as possible" after independence.
Meanwhile, Mr Salmond made clear that if the party succeeds in getting MSPs elected to Holyrood in Thursday's election, the party will put forward a motion instructing the Scottish Government to start independence negotiations with Boris Johnson.
The former first minister said: "If the people of Scotland back Alba on Thursday, in the first week we will lay a motion instructing the Scottish Government to commence independence negotiations with the UK Government. Then the Scottish Parliament can get on with the job of delivering independence."
He said to achieve this, Scotland would need "a refreshed independence platform", adding that Alba's new economic policy paper was a contribution to this "vital debate".
Meanwhile, economist Dr Walker argued that it was "time that the economic benefits of independence were recast for the post-Brexit age".
He stated: "Our policy set out today is Alba's proposal and one which we would urge the newly elected Scottish Government to adopt in the independence negotiations which we will ask parliament to instruct them to commence with the UK Government.
"Scotland's position will be immeasurably stronger if we negotiate inclusively as a Parliament with a supermajority for independence, not as a single political party."