Article 50(3) provides that the EU's treaties cease to apply to the withdrawing state when an exit agreement comes into force or two years has elapsed.
The EU's funding comes from what the Council calls its 'own resources', for which the treaties provide. Therefore two years from March 29th, the UK will not be bound by any previous commitments.
The EU will likely appeal to Article 70 of the Vienna Convention on the Law of Treaties:
1) Unless the treaty otherwise provides or the parties otherwise agree, the termination of a treaty under its provision..:
a) Releases the parties from any obligation further to perform the treaty; b) Does not affect any right, obligation or legal situation of the parties created through the execution of the treaty prior to its termination.
2) If a State denounces or withdraws from a multilateral treaty, paragraph 1 applies in the relations between the State and each of the other parties to the treaty from the date when such denunciation or withdrawal takes effect
So, Article 50(3) provides for a) but does not say a thing about b), unless that is interpreted as 'providing otherwise'.
If the UK failed to pay the EU before the withdrawal date, the UK would thus be obliged to pay that regardless of whether the UK is still in the EU.
So Britain is due for any payments obligated until Brexit day at the very least. I don't really see a situation where that woudl even be disputed.
The haziness surrounds agreements and obligations for payments made prior to withdrawla but only due after Brexit.
EU spending commitments typically look 3 years ahead, though can look further. Where the EU has made a commitment that straddles Brexit day, the EU's argument, on the basis of article 70 of the Conention is that this creates an obligation the UK has accrued prior to departure. As a side note, this logically means that any EU spending obligations in or to the UK would continue to apply, but as this is a net gain for Europe anyway, butthurt's were in the UK.
The counter argument to this would be that any committment to funding is made by the EU which is its own legal personality distinct from those of the member states, set out in Article 47 of the Lisbon Treaty. The EU's member states are not liable for the EU's obligations. Article 311 requires that the EU to "provide itself with the means necessary to attain its objectives". The EU does this through European Council's own resources mechanism. That provides and requires for payment to the EU by its member states, not states that are not bound by EU treaties.
To me, the UK has the upper hand, though it is certainly not clear cut.