Image Captions Create New Paragraph

I often place an image, aligned either left or right, in the middle of a paragraph, and this works fine, with the text wrapping around the image. But if I assign a caption to the image it breaks the layout by creating a new paragraph. This is hard to explain, but in mid-sentence (wherever I insert the image) a <p> is added to the code so that the remainder of the sentence is dropped down to the next line. This is a problem I’ve had with WordPress for years, regardless of the theme, and I’ve resigned myself to not using image captions at all. Is there a way to correct this?