"无火不成烟" can be translated into English as "No fire, no smoke."
This translation directly conveys the meaning that smoke cannot exist without fire, aligning with the original Chinese idiom's implication that a certain outcome or phenomenon typically has a corresponding cause.
Alternatively, depending on the context, you might also express a similar idea with phrases like:
"Where there's smoke, there's fire." (A more common English idiom implying that where there are signs of a problem, there is likely an actual problem.)
"Smoke cannot rise without fire." (A more literal and less common but still understandable translation.)
However, "No fire, no smoke." is the most straightforward and contextually appropriate translation for this specific Chinese idiom.