diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index f57199b1..4a6ec1be 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -4013,7 +4013,7 @@ static void ggml_vk_load_shaders(vk_device& device) {
             uint32_t nary_shmem = 2 * sizeof(int) * BLOCK_SIZE +
                                   sizeof(int) * device->subgroup_size +
                                   2 * sizeof(int) +
-                                  (BLOCK_SIZE / device->subgroup_size) * sizeof(int);
+                                  2 * (BLOCK_SIZE / device->subgroup_size) * sizeof(int);
             if (device->subgroup_arithmetic && device->subgroup_require_full_support && device->subgroup_shuffle && device->subgroup_ballot &&
                 nary_shmem <= device->properties.limits.maxComputeSharedMemorySize) {
                 ggml_vk_create_pipeline2(device, device->pipeline_topk_f32[i], "topk_f32_"+std::to_string(i), topk_nary_search_f32_len, topk_nary_search_f32_data, "main", 2, sizeof(vk_op_topk_push_constants), {BLOCK_SIZE, 1, 1}, {BLOCK_SIZE, device->subgroup_size, device->subgroup_size_log2}, 1, true, true, device->subgroup_size);
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/topk_nary_search.comp b/ggml/src/ggml-vulkan/vulkan-shaders/topk_nary_search.comp
index f794285e..0b757f38 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/topk_nary_search.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/topk_nary_search.comp
@@ -38,6 +38,7 @@ shared int counts[SUBGROUP_SIZE];
 shared int sh_min_idx;
 shared uint sh_total;
 shared uint offset_partials[BLOCK_SIZE / SUBGROUP_SIZE];
+shared uint eq_min_partials[BLOCK_SIZE / SUBGROUP_SIZE];
 
 // Map float values to uint such that comparisons still work.
 // Positive values set the high bit, negative values are inverted.
@@ -156,25 +157,66 @@ void topk(const uint row) {
         // We need to compact these values to the start of the dst_row array.
         // Have each subgroup count how many items it'll store, so other
         // subgroups can compute their base offset.
-        bool top = f2ui(intBitsToFloat(v.y)) >= range_min;
-        uvec4 b = subgroupBallot(top);
-        uint bit_count = subgroupBallotBitCount(b);
-        if ((tid % SUBGROUP_SIZE) == 0) {
-            offset_partials[tid / SUBGROUP_SIZE] = bit_count;
-        }
-        barrier();
-
-        uint out_idx = 0;
-        [[unroll]] for (int i = 0; i < BLOCK_SIZE / SUBGROUP_SIZE; ++i) {
-            if (i < tid / SUBGROUP_SIZE) {
-                out_idx += offset_partials[i];
+        // Values strictly greater than range_min must be stored. For values equal
+        // to range_min, there can be ties and it's possible we'll need to store
+        // an arbitrary subset of them.
+        // If total == p.k, have a fast path where we don't need to handle ties.
+        if (total == p.k) {
+            bool top = f2ui(intBitsToFloat(v.y)) >= range_min;
+            uvec4 b = subgroupBallot(top);
+            uint bit_count = subgroupBallotBitCount(b);
+            if ((tid % SUBGROUP_SIZE) == 0) {
+                offset_partials[tid / SUBGROUP_SIZE] = bit_count;
             }
-        }
+            barrier();
 
-        uint bit_count_ex = subgroupBallotExclusiveBitCount(b);
-        if (top) {
-            // TODO: Copy directly to the output?
-            dst_row[out_idx + bit_count_ex] = v;
+            uint out_idx = 0;
+            [[unroll]] for (int i = 0; i < BLOCK_SIZE / SUBGROUP_SIZE; ++i) {
+                if (i < tid / SUBGROUP_SIZE) {
+                    out_idx += offset_partials[i];
+                }
+            }
+
+            uint bit_count_ex = subgroupBallotExclusiveBitCount(b);
+            if (top) {
+                // TODO: Copy directly to the output?
+                dst_row[out_idx + bit_count_ex] = v;
+            }
+        } else {
+            bool top = f2ui(intBitsToFloat(v.y)) > range_min;
+            bool eq_min = f2ui(intBitsToFloat(v.y)) == range_min;
+            uvec4 b_top = subgroupBallot(top);
+            uvec4 b_eq_min = subgroupBallot(eq_min);
+            uint bit_count_top = subgroupBallotBitCount(b_top);
+            uint bit_count_eq_min = subgroupBallotBitCount(b_eq_min);
+            if ((tid % SUBGROUP_SIZE) == 0) {
+                offset_partials[tid / SUBGROUP_SIZE] = bit_count_top;
+                eq_min_partials[tid / SUBGROUP_SIZE] = bit_count_eq_min;
+            }
+            barrier();
+
+            uint out_idx = 0;
+            uint eq_min_base = 0;
+            uint eq_min_idx = 0;
+            [[unroll]] for (int i = 0; i < BLOCK_SIZE / SUBGROUP_SIZE; ++i) {
+                if (i < tid / SUBGROUP_SIZE) {
+                    out_idx += offset_partials[i];
+                    eq_min_idx += eq_min_partials[i];
+                }
+                eq_min_base += offset_partials[i];
+            }
+            // range_min values are stored at the end
+            eq_min_idx += eq_min_base;
+
+            uint bit_count_ex_top = subgroupBallotExclusiveBitCount(b_top);
+            uint bit_count_ex_eq_min = subgroupBallotExclusiveBitCount(b_eq_min);
+            if (top) {
+                // TODO: Copy directly to the output?
+                dst_row[out_idx + bit_count_ex_top] = v;
+            }
+            if (eq_min && eq_min_idx + bit_count_ex_eq_min < p.k) {
+                dst_row[eq_min_idx + bit_count_ex_eq_min] = v;
+            }
         }
 
         barrier();