Most interpretations of Hume's discussion of coherence are what we can call 'gap-filling interpretations'. Gap-filling interpretations take their cue from H. H. Price, who first proposed such an interpretation in his pioneering work, Hume’s Theory of the External World. Suppose I have an various occasions watched a fire burn down. In such a case I have a series of impressions that shade from brightly burning coals to dull ashes. We can designate these impressions by a series of letters,
A B C D E
where A is the impression of bright red burning coals, E is the impression of dull gray ashes, and B, C, and D are intermediate impressions. This series of impressions is taken to be continuous. On other occasions, however, my observation is interrupted. Instead of a continuous series I have an interrrupted one:
A . . . E
On a gap-filling interpretation we are moved by the resemblance between this interrupted series and the previous continuous series to fill in the gap with the missing impressions (B, C, & D). Because of this resemblance, and our consequent ability to fill in the gaps of an interrupted series, we say that the interrupted series is coherent. Price puts considerable emphasis on this point. There are a number of versions of gap-filling interpretations, but they tend to be variations on Price's basic theme.
Gap-filling interpretations have the advantage of being superficially plausible. They have the disadvantage of being wrong. There are a number of reasons why this is so.
The first and most purely exegetical reason is that gap-filling is a doubtful way to define coherence in Hume’s sense. In the passage I've already noted, Price attempts to do exactly this: two sense-impressions are coherent if we can perform this sort of gap-filling operation with them. It's very clear, however, that this is too narrow. Hume does not restrict coherence to 'gappy' series of impressions; in fact, Hume says that objects "have a certain coherence even as they appear to our senses." In other words, to recognize the coherence of our perceptions we don’t have to appeal to interrupted series at all; we recognize simply from our own experience, without performing any sort of operation on them, that there is a coherence in what we perceive. Nor is this in any way surprising. When Hume expands a bit on what he means by the coherence of our perceptions, he says that they have "a mutual connexion and dependence” and a “regularity of operation." We don’t have to find and fill gaps in our perceptions to recognize that there is some sort of regularity to the world as we perceive it.
[In the paper I give two more reasons why gap-filling won't work, and propose my own 'loose idea' interpretation.]