diff --git a/src/storage/src/source/generator.rs b/src/storage/src/source/generator.rs
index 5103454e19dac..f6216097555ac 100644
--- a/src/storage/src/source/generator.rs
+++ b/src/storage/src/source/generator.rs
@@ -113,7 +113,6 @@ impl SourceRender for LoadGeneratorSourceConnection {
             let Some(resume_offset) = resume_upper.into_option() else {
                 return
             };
-            cap.downgrade(&resume_offset);
 
             let mut rows = as_generator(&self.load_generator, self.tick_micros).by_seed(
                 mz_ore::now::SYSTEM_TIME.clone(),
@@ -139,7 +138,14 @@ impl SourceRender for LoadGeneratorSourceConnection {
                     }
                     Event::Progress(Some(offset)) => {
                         cap.downgrade(&offset);
-                        tokio::time::sleep(tick).await;
+                        // We only sleep if we have surpassed the resume offset so that we can
+                        // quickly go over any historical updates that a generator might choose to
+                        // emit.
+                        // TODO(petrosagg): Remove the sleep below and make generators return an
+                        // async stream so that they can drive the rate of production directly
+                        if resume_offset < offset {
+                            tokio::time::sleep(tick).await;
+                        }
                     }
                     Event::Progress(None) => return,
                 }