Having no budget does not mean you are innovative.
Innovative means having the budget to afford the things you must to survive.
Survival is being equal parts forward looking and retrospective. It's looking at and activating the new and the old with equal measure.
Budget. Plan. Afford. Curate. Innovate. Don't hoodwink yourself that the absence of a budget means you are innovative.
Oh and budgets are innovative when they are focused just as much on the future as they are on the past.