I found that at first, being vegan was more expensive. In reality though, I just had to spend more the first few weeks to get ingredients I never had used before (nutritional yeast, tamari, vegan mayo, all kinds of grains & nuts, etc.) I think any time you make a change in your diet, you are going to spend more at first just to get yourself started, and then things stabilize and got back to normal. I have a few tips to keep things on budget:
1) Start slow. Don't buy EVERYTHING at once.
2) Buy in bulk. I save soooo much money by shopping at Costco. Some things that are WAY cheaper there are nuts, olive oil, chia seeds, quinoa, rice, baking supplies like vanilla, sugar, coconut oil, etc.
3) Use dried beans. They are so much cheaper than canned! I soak them overnight and then cook them the next day (usually on a Sunday) and then freeze them in airtight containers. This way, you can make a giant batch and use them straight from the freezer for weeks. If you do it this way, you only have to cook beans from scratch once a month or so.
I have a post on my blog called "a week of vegan meals on a budget" that includes a grocery list and all the recipes for a week's worth of meals that is very inexpensive and easy to do. You can check it out at honeyandcardamom.com if you like