You don't actually mention what work he is doing in your initial post -- although you do mention that it is artwork in a later post. So, if you will excuse me, for the moment I'm going to pretend that we still don't know what the freelancer is doing.
There are three types/timings of payments: advanced, progress, and completion. Each solves a different issue.
The advanced payment exists to reduce risk on the part of the supplier. Will the client change their mind? Will they disappear? Will they not fulfill their promises? Will they not pay? By receiving a deposit up front (sometimes called a good-faith deposit) risk to the supplier is reduced.
Progress payments exist to reduce both the finance cost and risk associated with providing services or materials over a period of time. By receiving payments roughly as costs are incurred, the supplier avoids risk beyond what they are willing to invest and also avoids having to finance the full cost of providing the product. What appears to be an advanced payment is often a progress payment in disguise (for example when materials have to be special ordered).
Finally, completion payments exist to protect the purchaser. Often these are called hold-backs or guarantees. But they are always paid after the final delivery of the finished product.
Why is all this important?
All industries have a standard recognition of the risk balance involved (aka a standard payment scheme).
For example, in small construction the payments (generally) consist of an initial combined progress (covering ordering the materials) and advance payment and a completion payment. So the risks being covered are largely associated with one or either party not completing the contract.
In large construction, however, the payments generally consist of progress and completion payments. The risk of the customer not completing is covered off by the guarantor. The payment scheme instead is focused on reduced finance costs and supplier completion risk.
The point is that your contract needs to provide for all three risk/cost types in order to be fair. Typically, the industry standard will provide the base for a normal relationship between them. You need to be aware of what constitutes a sufficient variance between them to justify a different payment scheme (the difference between large and small construction being an example). To be fair your contract needs to allow for these oddballs.
Now to apply it to artwork. (For those of you wondering about the use of a week -- most artists (even commercial ones) earn below the poverty line. Waiting three weeks for payment is about the limit.)
Artwork is a nebulous term (my wife is an artist). A piece may take an hour or it may take months. There is a high risk that the client will bail (or more likely just not pay) and there is a high risk of the artist not delivering. So a mix of the advance and completion payment schemes are almost an automatic. Whether a progress payment is needed depends on the length of the project.
If you are expecting commissions to take under a week then payment on completion is appropriate (presuming there are sufficient guarantees of payment). And your contracted payment scheme will reflect that.
The point is that if a commission suddenly takes a month to complete, another scheme (progress) is more appropriate. And you may have to create milestones to balance the associated risks.
Your contract needs to provide an upper limit in order to be fair. At what point does an alternate payment scheme kick in?
That means that you need to be somewhat flexible with your existing contract.
Having said that, it doesn't mean paying in advance because the artist is in debt. It means adjusting your payment scheme appropriately to the length of the task set.
So ultimately, you need to negotiate between the two of you. Is the work involved legitimately over the limit (in which case you need to partial pay)? Or is this just a case of poverty sucks? (In which case, you're decision is much more complex).
In any case, full payment just isn't on since it leaves you with the full risk of his not completing the work.