The Conservatives have rejected calls from Nick Clegg to tighten controls over free schools.
The Lib Dem leader accused the Tories of failing to enforce "basic standards" in schools as he dramatically disowned key planks of the coalition's education policy.
But Conservative education minister Elizabeth Truss told the BBC it was a "shame" some Lib Dems did not back free schools.
She said the "whole point" of the schools "is they have these freedoms... that's what's helping them outperform maintained schools".
"You shouldn't kill of the goose that's laid the golden egg."
Nick Clegg will launch a dramatic attack on Michael Gove's "ideological" free schools policy in a speech next week, and remind voters that the two coalition parties have differing visions on education reform.
The Deputy Prime Minister is to open dividing lines with the Tories by insisting all teachers should be qualified, and the national curriculum should be taught in every school.
"I'm proud of our work over the last three years to increase school autonomy, which, in Government with the Conservatives, has been through the academies programme," the Liberal Democrat leader will say.
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"And it is Lib Dem policy to give all schools, whether they are academies or not, those same freedoms to attract and reward excellent teaching, set their own term dates and vary their school day.
"We believe greater autonomy enables school leaders to take responsibility in those areas where they know what's best for their pupils, whilst also giving them the freedom to innovate.
"But it shouldn't surprise you if I say that, although we work well with the Conservatives, our two parties still have differences of opinion, some strongly held.
"Looking to the future, there are aspects of schools policy currently affected by the priorities of the Conservative Party which I would not want to see continue.
"For example, whilst I want to give schools the space to innovate, I also believe every parent needs reassurance that the school their child attends, whatever its title or structure, meets certain core standards of teaching and care. A parental guarantee, if you like.
"Parents don't want ideology to get in the way of their children's education.
"They don't care about the latest political label attached to their child's school. What they want, and expect, is that their children are taught by good teachers, get taught a core body of knowledge, and get a healthy meal every day."
Truss's sentiments were echoed by the party's former minister in the Home Office.
Jeremy Browne said that while education standards in the UK continued to lag behind those of other industrialised nations that it was right to look outside the status quo.
The Taunton Deane MP said: "Well I support free schools. I think free schools are a small "L" liberal policy."
But Browne, who was axed from his job as Home Office Minister by party leader Nick Clegg in the reshuffle on October 7, warned his party against succumbing to "instinctively statist" behaviour.
He told the BBC's Sunday Politics: "I think there are two big dangers for us as a party.
"I don't think we should be: one) instinctively statist, and I don't think we should two) be instinctively in favour of the status quo.
"I want us to have a restless, radical, energetic, liberal, reforming instinct that is about putting more power and responsibility and opportunity in the hands of individual people."
Browne also said it would be "a mistake" for the party to shift to the left.
Asked if he thought the Liberal Democrats were shifting politically, he said: "I think there is a danger, when a party or any organisation feels that it's in a difficult position, to look inwards, to look for reassuring familiar policy positions.
"And what I don't want is for us to be the party that looks inwards and speaks to the 9% of people who are minded to support us already. I want us to look outwards and speak to the 91% of the population, whom I think we have a good story to tell about the contribution that we have made to getting the deficit down, to keeping interest rates low, to cutting crime in this country."
He added: "I want us to be unambiguously and unapologetically an authentic liberal party. I don't want us to feel that we have to echo the policy decisions of the Labour left, I don't want us to needingly crave the approval of columnists like Polly Toynbee (of the Guardian), I don't want us to be a pale imitation of the Labour Party.
"I think we should be proud and unambiguously an authentic liberal party; that is my ambition for the Liberal Democrat Party."
Veering to the left, said Browne, would be "a mistake; I think we should be on the liberal centre ground".
Amid claims that the Liberal Democrats were wooing Labour voters, Browne was also asked if he was himself being wooed by the Conservative Party.
Browne, who is universally acknowledged to be to the right of his party, revealed in an interview with The Times that he had been approached by senior Tory figures.
He told the Sunday Politics programme that "generous suggestions" were made during his conversations with those Tories, but that he had no plans to join another political party.
He said: "I don't know if wooing me is the right word.
"I've been reported, and I've said myself, that the Conservatives have made some advances or made some generous suggestions to me.
"I am a liberal and I am a Liberal Democrat. I have been a member of the Lib Dems since the party was founded and I joined when I was 18 years old, and I have campaigned extremely vigorously and tirelessly for the Liberal Democrats for my entire adult life, so I am not about to go and join another political party."
A Department of Education spokesperson said: "Free schools are raising standards and giving parents more choice.
"They are run by teachers - not local bureaucrats or Westminster politicians - and are free to set their own curriculum, decide how they spend their money and employ who they think are the best people for the job. This Government is not going to take these freedoms away.
"Independent schools have always been able to hire brilliant people who have not got QTS. Free schools and academies now have the same freedoms as independent schools to hire great linguists, computer scientists, engineers and other specialists so they can inspire their pupils."